Unfoldings
Submitted to the Department of Architecture
in partial fulfillment of the requirements
for the degree Master of Science in Visual Studies,
at the Center for Advanced Visual Studies,
Massachusetts Institute of Technology
June, 1992
Caryn L. Johnson
Bachelor of Science, Yale College
New Haven, Connecticut, June, 1982
Signature of Author
yn L. Johnson
Photograph by Traci Daniels, 1991
partment of
itecture, May 8, 1992
Certified by _
Paul Earls
Lecturer, Department of Architecture
@Caryn L. Johnson 1992. All rights reserved.
Accepted by
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Table of Contents
A bstract ........................................................................
7
Introduction .........................................................................
9
10
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Acknowledgments .............................................................
13
Characteristics of Play ............................................................
Huizinga's Analysis of Play ................
14
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14
Play and Volition ..................................................................
Play and "Real Life" .....
15
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19
Play and O rder ....................................................................
Playful Response .............................................
Endgam e .............................
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The Play Experiment .....................................................................
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Session 1: Unstructured Play ........................................
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Session 2: Structured Play ...........................................................
Session 3: Discussing Play .....................................
23
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29
Unfoldings
Analysis of Questionnaire Responses ...............................................
Conclusions .........................
34
Chapter References ........................
36
Figure Credits ............................
37
The Role of Play in the Visual Arts .........
39
Play Sculptures ...........................
40
Space-play ................................
45
Trompe l'Oeil and Anamorphosis ......
45
Non-Objective Art and Concrete Art ....
47
Op Art and Spatial Ambiguity .........
49
Time-play ...............................
51
Op Art and Temporal Ambiguity ......-
52
Kinetic Art: Mobiles and Transformables
53
Chapter References .........................
59
Figure Credits ............................
60
Framework ................-...........
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A Personal Conception of Form ..............
Visual Pattern .......
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Symbolic Forms .....................
Linear and Planar Figures .............-
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Planar Jitterbugs: Meditations on the Square ...
Beyond the Plane ...................
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The Symbolism of Jitterbugs ... . . . . . . . . . . . . . . . .
Chapter References .................
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Figure Credits .....................
Jitterbug Sculptures ................
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M irage ............................
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Jitterblocks
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The making of Jitterblocks .....
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Chapter References .................
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Bibliography ......................
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Arts and Artists................
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Mathematics in Art; Perspective; Patter
Mathematicians and Mathematics...
Philosophy, Science, and Cosmology
Play, Toys, Games, and Puzzles .....
M iscellaneous ....................
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Index .............................. Index...........................00
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101
Unfoldings
Unfoldings
by Caryn L. Johnson
Submitted to the Department of Architecture on May 8, 1992,
in partial fulfillment of the requirements for the degree of Master of Science in Visual Studies
Abstract
Unfoldings examines connections between play, visual art,
and mathematics.
Huizinga's analysis of play, described in his text Homo
Ludens, is compared to the creative process in art-making
and to the creative response of the viewer. The play
process is examined through questionnaire responses and
observations made during an evening of experimental
play.
Huizinga's assertion that play is not a factor in the plastic
arts is challenged. Refutations and counterexamples
drawn from the history of art since the Renaissance show
that play is indeed a factor. The artistic movements cited
are those which provide examples of works having either
particularly playful or particularly mathematical content,
or both, including Anamorphic painting; Dada; Bauhaus;
Neo-Plasticism; Concrete Art; Op Art; Fluxus; and Kinetic
Art. Special attention is given to the works of Alexander
Calder, George Rickey, and Yaacov Agam.
The author describes a personal iconography, and
introduces the geometric foundation of her sculptural
works, which derive from the geometry of R. Buckminster
Fuller's "vector-equilibrium jitterbug." Descriptions,
photographs, and drawings are included for the author's
Thesis Project, comprising several kinetic, manipulatable
jitterbug sculptures.
Paul Earls
Thesis Supervisor:
L
ment of Architecture
Read
Arthur Loeb
Professor of Visual and Environmental Studies
Harvard University
Unfoldings
Introduction
My artistic work centers around the meeting point of
mathematics, visual art, and play. The blurring of
dividing lines among these modes is my inspiration,
prompting me to consider such questions as:
" When does a sculpture become a toy? Particularly,
when does a geometric kinetic sculpture become a
mathematical toy, and what is the power of that toy/
sculpture to prompt discovery, to become a tool for
understanding space?
- What is the role of play in the creative process, and in
the viewers' response to artistic works, particularly to
works with strong mathematical content?
* Do artists inform and teach through play? Do spectators learn through play?
* How do artists whose work is fundamentally geometric, or who employ geometric symbolism, analyze and
discuss the geometric content and concepts of their
work?
e
Are there deeper meanings to other artists' geometric
icons as there are in my own work?
Most people do not see mathematics and art as having
any connection. I view mathematics as a collection of
specialized languages for discussing, in the abstract and
as precisely as possible, characteristics of the observed
world, and characteristics of "logically possible" worlds.
Algebra is a language for describing quantities and their
combinations, geometry is a language for describing the
attributes of space and dimension, the calculus is a
language for discussing the characteristics of change, and
so on. These languages have their origin and foundation
in observations of relationships in the real world on the
one hand, and in the development of logic and discursive
reasoning on the other hand. The visual arts have their
foundation in the process of representation of worldly
objects and phenomena on the one hand, and in intuitive,
purely conceptual creative actions on the other hand.
Anything that shifts between these modes must merge
the rational with the intuitive, the logical with the
extra-logical.
I posit that play is one such bridge, that it is a
fundamental activity permeating all cultural forms, and
an essential element of the creative process in the visual
Unfoldings
arts. I also posit that, when an artistic work provokes a
playful response in the viewer, the viewer's experience of
that work changes. I test this thesis against the opinions of
a number of artists whose work is related to or has
inspired my own, as well as comparing it to the responses
of a group of test subjects.
My sculptures-hinged geometric sculptures in wood,
plastic, metal, and glass-are human-scale, some
intended to be held in the hands, some to be moved using
the whole body. They continually shift across the line
dividing sculpture from toy, sculpture from mathematical
model.
The elements of my sculptures derive from branches of
mathematics that deal with form and dimension:
geometry and group theory (the branch of mathematics
that categorizes spatial symmetries). Other mathematical
disciplines dealing with space-topology and relativity,
for example-have greatly influenced the field of visual
arts, for investigations in these disciplines complement
artistic explorations of figurative representation and
perspective, of distortion and twist, of time as an artistic
dimension, of symmetry and asymmetry in decorative
pattern and in composition, and of the visual power of
pure form. I posit connections between play and the
artistic expression of these influences.
This thesis results from an on-going inquiry into these
questions. The territory I am exploring is rich, and what
follows is a record of the results of my prospecting in a
favorite lode.
Acknowledgments
I owe an enormous debt of thanks to a great many people
who have helped me along the path that has led to this
exploration and this thesis. Some have guided, some have
accompanied me, and some have gotten behind me and
pushed when I didn't think I could go any further. To all
of those people, I offer my heartfelt gratitude. Were I to
list all of their names, the list would be nearly as long as
the thesis itself, but I must express my written thanks to a
crucial few:
my advisors, Otto Piene, Arthur Loeb, and Paul Earls, whose
example and advice I have so very much appreciated and
attempted to follow;
my fellow students at the Center for Advanced Visual
Studies: Greg Haun, Nathan Hemenway, Sue Mie Kim, Chris
Kirwan, Iris Oliveras, Maggie Orth, Nina Papa, Dan Spikol,
Marta Vahtar, Diane Willow, and Zafos Xagoraris, plus the
rest of the Center's "cast and crew," whose criticism and
suggestions have done so much to help me both refine and
broaden my artistic vision;
fellow explorers and experimenters who showed that the
road was worth travelling and paved some part of the way,
Cynthia Col, Lance McKee, Stu Coffin, Jack Gray, and Carol
Strohecker;
all those who helped me with the mechanics of organizing,
building, and writing over the two years of the Master's
program, especially Pam and Dennis Rockwell, Anne Starr,
Chris Dewart, Jason Dickerson, Traci Daniels, Woodie
Flowers, David Gossard, Harry West, the owners and
employees of countless hardware stores, marine suppliers,
plumbing suppliers, optical shops, sporting-goods stores,
stained-glass shops, art-supply stores, plastics and polarizedfilm suppliers and manufacturers, lumberyards, photo shops,
and hobby shops;
Introduction
my friends and sponsors at Sun Microsystems Computer
Corporation, who provided a terrific working environment,
daily support and encouragement, and whose willingness to
accommodate my crazy schedule made the two years of
school possible, and whose donation of access to disk space
and to FrameMaker publishing software made the thesis
itself possible in the timeframe and format I required;
all the friends who have dropped by the studio and the shop
to see work in progress, and who came to shows, and who
looked at sketches, models, slides, and photographs (no
matter how blurry), and who gave me comments, criticisms,
and encouragement;
and, last but foremost in my heart, my family, both the one
God so wonderfully provided, and the ones that have
gathered me in as kin: my darling Jeff, Mom, Dad, Kim, and
all the relatives who are distant but close to my heart, Jeff's
wonderful family, Peter, Jennifer & Jim, and my
"MASSCOMP family."
Unfoldings
Characteristics of Play
In examining the meeting point of art, geometric
mathematics, and play, I investigated play first. I find play
very closely related to creativity both in character and in
action, and sought substantiation of that view. I wanted to
understand what play means to the participants in a
game, to examine the aspects of play that come into the
creation of a game, a toy, or anything else to which people
respond in a playful manner, and then to consider the
aspects of geometry that connect to art/play.
The seminal work in this field is Homo Ludens: A study of the
play element of culture, by Johan Huizinga. I find most of
Huizinga's account accurate, succinct, and compelling in
its descriptions of the fundamental characteristics of play
in its many forms and aspects. Huizinga exposes the play
characteristics of myth, ritual, language, law, philosophy,
and war. He demonstrates ties between play and poetry,
play and music, play and dance. In all of these pursuits he
shows that the power of play to introduce order, to make
the mysterious in some way comprehensible and to move
the players outside the ordinary into the mystical, is an
essential feature separating out particular subsets of these
social forms. Huizinga's analysis is not flawless, however.
"Haiti,1950"
Unfoldings
Huizinga's Analysis of Play
Play and Volition
Huizinga sets out to show that "genuine, pure play is one
of the main bases of civilization" and that play falls
among human pursuits as a "special form of activity:"
Regarding the assertion that play is voluntary, Huizinga
claims:
existing before culture itself existed, accompanying it and
pervading it from the earliest beginnings right up to the
phase of civilization we are now living in. [1]
Huizinga examines the characteristics of play, the aspects
of play that make it significant for the players, that
separate it as an activity from the rest of life, while trying
to, as he puts it, "avoid the philosophical short-circuit that
would assert all human action to be play."[2] Unlike
researchers in biology and psychology, who seek a
physiological or a psychological basis for play, Huizinga
seeks to discover what it is about play that makes it "fun,"
just as I have. In play's diverse forms, he finds the
following four essential characteristics:
e
play is voluntary
e
play takes the participants outside of "ordinary" or
"real" life
e
play is separated from ordinary life in space and time,
taking place in its own "magic circle"
e
play creates order.
I summarize Huizinga's justifications for these
propositions and add comparisons to the creative process
in the sections below.
Play to order is no longer play: it could at best be but a
forcible imitation of it. By this quality of freedom alone, play
marks itself off from the course of the natural process.... It is
never a task. It is done at leisure, during "free time." Only
when play is a recognized cultural function-a rite, a
ceremony-is it bound up with notions of obligation and
duty. [31
Thus one cannot be compelled to either create or join the
magic circle of normal play-being coerced into playing
takes the fun out of it. In ritual, there are other elements
'coming into play,' so to speak, as the community gathers
for the purpose of commemorating or anticipating some
real or mythic event, participating in that event through
the special means of re-presentation or symbolic
foretelling. Participation in such ritual is an extension of
participation in society as a whole: members of the society
are expected to share in rituals in the same way they are
expected to share in the other tasks of community life.
Though Huizinga does not discuss the perspective of the
outsider, one cannot demand entrance to the magic circle
either, as that is tantamount to demanding that those
involved in the game "play to order" for the one who
wishes to join.
It is possible, however, to invite or entice someone into
play, to join the game, and it is possible for an outsider to
request to join. The invitation or the request, and the
response on either side, must be done delicately, or else
the spell of play is broken. Entering the game means both
accepting, and being accepted into, a special, temporary
Characteristicsof Play
society created by the players. This invitation and
acceptance have a special bearing on the role of play in
the visual arts, as the material in the following chapter
demonstrates.
Play and "Real Life"
The separation of play activity from "ordinary" life is, in
Huizinga's terms, a distancing in both thought and
action:
[it is] a stepping out of "real" life into a temporary sphere of
activity with a disposition all of its own.... It stands outside
the immediate satisfaction of wants and appetites, indeed it
interrupts the appetitive process. [It is] an intermezzo, an
interlude in our daily lives. [4])
The word interlude is curiously self-referential here, the
Latin meaning being "in the midst of play." In a way, this
statement presents play as a subtext of life-as-play, which
robs the magic circle of its specialness, threatening to
create the short-circuit Huizinga was trying to avoid. But
the sense of the passage is clear. In play, one forgets, for a
while, life's headaches and obligations, and allows
imagination to redefine aspects of self, shape, and
situation.
In this sense, play is transportive, leading the player out
of the realm of normal thought and behavior, permitting
the participants in the game to act in ways that are not
necessarily dependent on either instinct or logic, but are
instead based on imagination and intuition. Huizinga
comments:
Nevertheless, .. the consciousness of play being "only a
pretend" does not by any means prevent it from proceeding
with the utmost seriousness, with an absorption, a devotion
that passes into rapture and, temporarily at least, completely
abolishes that troublesome "only" feeling. Any game can at
any time wholly run away with the players. [5]
This is an aspect that play has in common with the
creative process, with the products of intuition. Art is
inherently intuitive, and cannot be reduced to the purely
rational; even when the artist apparently starts with the
ordinary stuff of life, and with ideas grounded in the
everyday, the logical, and the rational, it is actually the
process of invention, of selection and juxtaposition
according to intuition and aesthetic judgment, of imbuing
the forms with symbolic meaning and divesting them of
their functional character that lifts the result out of the
realm of the ordinary, beyond the realms of illustration,
craft, and design, and into the realm of art. Thdo van
Doesburg recognized that this is not a logical, theoreticdiscursive process:
One of the most serious of the many reproaches leveled
against modem artists is that they address themselves to the
public not only through their works, but through their words
as well....
This is the source of the misconception that the modern artist
is too much of a theoretician and that his work springs from a
prioritheories. In fact, precisely the opposite is the case. The
theory came into being as the necessary consequence of
creative activity. Artists do not write about art, they write from
within art. [61
The artist, and particularly the modern artist, sees nature
creatively in that he gives form to his experience through
pure artistic means, not arbitrarily, but according to the
logical laws of his branch of art (these laws are the means of
controlling creative intuition). [7]
Art-making is therefore either a form of play, or is closely
related in character-another activity that can wholly run
Unfoldings
away with the participant, as perhaps it has in the
following image:
Huizinga presents this aspect of play as the physical
analogue of the spiritual distancing described above. As
the psychic character of play is special, extra-ordinary, so
the physical aspects, space and time, are invested with
special status.
However, though the physical space of play is special, I
disagree that the playspace actually needs to be that
physically distant from areas of normal activity. In fact,
play in the open takes on a special atmosphere-it is bold,
it is adventurous, it challenges those nearby folk who are
engaged in normal pursuits to dare to step out of the
mundane.
Huizinga comments on the importance of boldness, of
risk in play:
"Dali Atomicus"
Huizinga continues:
Play is distinct from "ordinary" life both as to locality and
duration. It is "played out" within certain limits of time and
place.
Play begins, and then at a certain moment it is "over."...
While it is in progress all is movement, change, alternation,
succession, association, separation.
More striking even than the limitation as to time is the
limitation as to space. All play moves and has its being
within a playground marked off beforehand either materially
or ideally, . . . forbidden spots, isolated, hedged round,
hallowed, within which special rules obtain,... temporary
worlds within the ordinary world, dedicated to the
performance of an act apart. [8]
To dare, to take risks, to bear uncertainty, to endure tensionthese are the essence of the play spirit. Tension adds to the
importance of the game and, as it increases, enables the
player to forget that he is only playing. [9]
Playing in public may, in fact, change the attitude of the
players. They may think not "we are only playing," but
"everyone else is only going about their business,"
turning play into celebration, as in the two images below
by Dolf Kruger and Alexander Calder.
.ft
Characteristicsof Play
"Rapenburgerstraat"
Firemen's dinnerfor Brancusil
Is the physical distance Huizinga describes also an
element of the creative process in the visual arts? Does the
artist separate himself or herself from the ordinary world,
entering a "temporary world within the ordinary world,
dedicated to the performance of an act apart"?
However, within the past century, various trends have, in
some measure, dissolved the walls around the artist. The
Traditionally, until the past century or so, the answer has
been yes. The artist worked within a studio, or a salon, in
order to create without distractions, to set up models and
lighting where they would not be disturbed, and to keep
from contaminating art materials with everyday materials
and vice versa.
1. In a Greenwich Village restaurant decorated with a
papier-mach6 horse's head, murals and a firemen's pole,
Calder and a group of Whitney Studio Club members
cavorted in honor of Brancusi's exhibition at the Joseph
Brummer Galler, New York City, November 1926. Clockwise
around the table are seen Alexander Brook, Yasuo Kuniyoshi,
an orating Louis Bouche, a leaping Calder, Niles Spencer,
Walt Kuhn, an unidentified figure, Donald Greason, another
unidentified figure, Edmund Duffy, Art Young, and, on the
pole, the athletic artist-brothers Robert and Charles Howard
1101
Unfoldings
whole of 20th century art is filled with movements whose
stated aim was to take art out of the museum and salon,
out of the studio, to intentionally contaminate art
materials with everyday materials-to make everyday
materials themselves into art materials. Art schools and
circles of artists strove to take access to art out of the
province of the elite, to connect the artist to the common
citizen, to show that, in fact, the common citizen could be
a maker of art, to apply the methods and intuitions of art
to the creation of everyday things, and to make everyday
activities into art activities, into "acts apart." Consider
these descriptions of the foundations of Dada, the
Bauhaus, and Fluxus:
Dada:
It is hardly surprising that the mechanized mass killing of the
First World War should have driven [Marcel] Duchamp to
despair. Together with a number of others who shared his
attitude, he launched in protest a movement called Dada....
Dada has often been called nihilistic, and its declared
purpose was indeed to make dear to the public at large that
all established values, moral or aesthetic, had been rendered
meaningless by the catastrophe of the great war. During its
short life, . . . Dada preached non-sense and anti-art with a
vengeance.
Yet Dada was not a completely negative movement. In its
calculated irrationality there was also liberation, a voyage
into unknown provinces of the creative mind. The only law
respected by the Dadaists was that of chance, and the only
reality that of their own imaginations.... Playfulness and
spontaneity are ... the impulses behind Duchamp's
Ready-Mades, which the artist created simply by shifting
their context from the utilitarian to the aesthetic... That
artistic creation depends neither on established rules nor on
manual craftsmanship . . . is an important discovery. [11]
Bauhaus:
Although the Bauhaus changed direction several times
during its short life, it initially pursued three main aims....
The school's first aim was to rescue all the arts from the
isolation in which each then (allegedly) found itself, and to
train the craftsmen, painter and sculptors of the future to
embark on cooperative projects in which all their skills
would be combined.
The second aim was to elevate the status of the crafts to that
which the 'fine arts' then enjoyed. 'There is no essential
difference between the artist and the craftsman' the
Manifesto proclaims. 'The artist is an exalted craftsman...
Let us then create a new guild of craftsmen without the
class-distinctions that raise an arrogant barrier between
craftsman and artist!'
The third aim.. . was to establish 'constant contact with the
leaders of crafts and the industries of the country.' [12]
The Fluxus Manifesto:
PURGE the world of bourgeois sickness, 'intellectual,'
professional & commercialized culture, PURGE the world of
dead art, imitation, artificial art, abstract art, illusionistic art,
mathematical art-PURGE THE WORLD OF
'EUROPANISM'!
PROMOTE A REVOLUTIONARY FLOOD AND TIDE IN
ART. Promote living art, anti-art, promote NON ART
REALITY to be grasped by all peoples, not only critics,
dilettantes and professionals.
FUSE the cadres of cultural, social & political revolutionaries
into united front & action. [13]
Fluxus artists in particular pursued the goal of making
not only works of art but the creative tools for making art
available to the masses through their FLUXKITs and
Characteristicsof Play
FLUXYEAR boxes, described more fully in the next
chapter.
Various 20th century artists have felt the need to go out
into the world to make art, to capture the essence of
things as they happen, as Walker Evans did when he
photographed passengers on the New York subways.
Alexander Calder went out into the world to create both
out of desire and out of necessity:
he had no studio, he lived and worked out of doors; already
he sought action, light and movement. He was enthralled by
the circus, the zoo, sporting events (Six-day Bike Race), and
parties (Firemen's Dinner for Brancusi and The San Regis
Restaurant). [14]
Like Evans, Calder made the daily commuter into one of
his models:
You folded a sheet of [a certain wrapping paper] into eight
rectangles and it would fit in your pocket. With this we used
to pass our time drawing people in the subway on our way to
and fro. [15]
But he also felt the need for a workspace set apart from
daily concerns, beginning with the workshops his family
provided him throughout his childhood and young
adulthood, and later his studios and workshops in France
and the United States.
Hence art-making, like play, can be an intermezzo
pursued in the special atmosphere of the studio but can
also be 'an act apart' performed in the midst of worldly
bustle.
Play and Order
Huizinga states:
Inside the play-ground an absolute and peculiar order
reigns.... Into an imperfect world and into the confusion of
life it brings a temporary, a limited perfection 2 . Play demands
order absolute and supreme. The least deviation from it
'spoils the game,' robs it of its character and makes it
worthless. [16]
I agree with the proposition stated here, but I have a slight
criticism of this passage-Huizinga has written it such
that he has avoided discussing who or what imparts the
order to the game. My hypothesis is that it is the game's
inventor and its participants (who may themselves be the
inventors) who mutually create and maintain the order
Huizinga describes for the duration of the game. 'Order'
here means two things: first, the existence of a set of rules
for the behavior of players and the manipulation of
objects (or, in the case of some games, Twenty Questions,
for example, the "manipulation" of concepts), which I
think of as the "structural order" of the play-circle, and
second, the actual conformance of the players to the rules,
which I think of as the "social order" of the play-circle. In
other words, play succeeds only when the players know
what they are to do and are doing it.
This touches upon my definition of the difference
between a game and a toy, which has to do with both the
physical qualities of the elements of the game or toy, and
with the player's interpretation of the rules associated
2. By perfection and order Huizinga does not mean "predictability." He makes it clear that a game one can always
win is no longer fun.
Unfoldings
with those elements. In a game, the inventor has provided
a specific set of rules that go beyond the pure formal
possibilities of the game pieces, or in which there are no
physical pieces at all, and the player or players try to
follow those rules. In the case of a toy, the original
inventor has provided an object, sometimes with a set of
rules, or with suggestions for the method for play, but the
player or players feel free to create new ways of playing
with the object, or to create toys from objects not intended
as toys (in which case they are themselves the inventor of
the toy). The new ways of playing with the object are
based on any or all of the following:
the shape(s) of the pieces of the toy, or things that the
shape suggests to the players
This is the case when a player uses a stick as a wand; a
sceptre; a conductor's baton; a twirler's baton; a
sword; a strut for a kite; a stylus for drawing shapes in
the sand or in the snow; and so on.
ChristopherRobin knighting Pooh
* an idea a player comes up with that has little or
nothing to do with the formal aspects of the object, but
for which that object will serve because it is either
related conceptually to the player's idea, or, simply,
because the object happens to be at hand
In this case, a player might use a stick as an object to
tease a cat with, or as an object to throw for a dog to
retrieve. Another example would be to use any object
as a playing piece for something else, such as the shoe
and hat pieces in Monopoly-the fact that they are
shaped as they are has nothing to do with their
meaning in the game, and any two small objects with
distinct shapes would serve just as well. The object is,
in a sense, a toy within a game. Here is an example:
Characteristicsof Play
It did. It kept on doing it .. .and when he went home for tea,
he had won thirty-six and lost twenty-eight, which meant
that he was-that he had-well, you take twenty-eight from
thirty-six, and that's what he was. Instead of the other way
around.
And that was the beginning of the game called Poohsticks,
which Pooh invented, and which he and his friends used to
play on the edge of the Forest. But they played with sticks
instead of fir-cones, because they were easier to mark. [17]
Though A. A. Milne described this in the context of
fiction, this is the process one goes through in real life of
discovering a principle, and deciding to use it.
A game of Poohsticks
[Pooh] had just come to the bridge; and not looking where he
was going, he tripped over something and the fir-cone jerked
out of his paw into the river.
"Bother," said Pooh, as it floated slowly under the bridge,
and he went back to get another fir-cone.... But then he
thought that he would just look at the river instead,. . . so he
lay down and looked at it, and it slipped slowly away
beneath him ... and suddenly, there was his fir-cone slipping
away too.
"That's funny," said Pooh. "I dropped it on the other side,"
said Pooh, "and it came out on this side! I wonder if it would
do it again?"
These two aspects of invention-shaping objects
according to a concept on the one hand and creating a
concept according to the suggestive power of a shape on
the other-are the essence of the creative act, the process
underlying image-making and sculpting. The artist either
finds a suggestive form within an existing image, a block
of wood or stone, a collection of objects, and builds upon
that form (as in Picasso's "Bull's Head," Duchamp's
"Ready-mades," or Calder's "Dog"), or begins with an
idea and molds materials chosen to match that concept
into a visual manifestation of the idea. The latter case is
the more common one, but, as an example of the former
case, Marchesseau notes:
Calder's early [carved] wood sculptures show that he began
by seeking in the shape of a stump the outlines that were best
suited to the individual sculpture. This concern led him to
rough out various caryatids and the curious figure of Saint
George Slaying the Dragon. [181
Thus, a person inventing ways of playing with a toy is an
artist of a kind, though the object thus produced, the toy,
serves a purpose different from the sculptor's creation.
Unfoldings
Dog, by Alexander Calder, 1940
~
Bull's Head by Picasso
I
The idea that playing with a toy could be an expression of
an inner artistic impulse was at the foundation of
Baudelaire's 1853 article in Le Monde Litteraire, titled "La
morale du joujou" (The moral significance of playthings)
in which he commented,
"a plaything is a child's first introduction to art, or rather, its
first manifestation, and once he reaches adulthood, no other
manifestation of art will fill his heart with the same warmth,
the same enthusiasm, the same confidence." [19]
Playful Response
Having investigated creativity in art-making, I began to
research playful responses to artwork, for the work serves
as the invitation to join the magic circle, and, as
mentioned
1r, the invitation must be carefully made
and freely accepted.
Characteristicsof Play
Frank Popper writes, in his beautiful monograph on
Yaacov Agam,
In the postwar world, the cultivation of the play instinct was
stimulated by the activity of the early 1950s. At the same time
as the German progenitor of Concrete poetry, Eugen
Gomringer, was putting forward his idea of the poem as
Spielraum (area for play), Again was developing a highly
original attitude toward play in connection with the plastic
arts: he was inviting the spectator to abolish the traditional
antinomy between contemplation and action.
His work . .. may be considered a stimulus to that
specifically human creativity that the spectator possesses as
well as the artist. For Agam, every human being is equal
before the work, and there is no sense in which the highly
cultivated or the highly intelligent should be regarded as
privileged with respect to it. But at the same time each
human being who participates in the work is engaging in the
highest possible human activity, that of creation. [20]
Agam is by no means the first artist to express the idea
that the creativity of the spectator is as fundamental to the
success of a work as the creativity of the artist. In 1917 van
Doesburg wrote
the observer himself shares inwardly in the creation and to
this extent the process may be described as a new re-creation
in the consciousness of the observer. This, the creative way, is
the only true way of looking at visual art. There is none other,
either for classical or for modern art.[21]
In other words, the viewer cannot simply look at a piece
passively, but must literally re-act toward the work,
exploring and discovering the same visual territory as the
artist who made the work in the first place.
Salvador Dali describes his sudden awakening to the
magic of paintings through this same creative response:
I was eating ... all by myself, when I suddenly saw the
pictures. They were the work of Ram6n Pichot, who at the
time was painting in Paris and much involved with
Impressionism. I gazed in fascination at the spots of paint,
apparently put on without any order, in thick layers, that
suddenly shaped up magnificently, in one got the right
distance away, into a dazzling vision of colors that
communicated a deep, sun-soaked image of a stream, a
landscape, or a face. I think my eyes were popping out of my
head. Never had I experienced such a sensation of
enchantment and magic. That, then was art! (Unspeakable p.
42*)
Endgame
"Play begins, and then at a certain moment it is over" (see
quote on page 16). Huizinga doesn't spend much time
discussing how one returns to 'real life' from the play
world. From my observations, I conclude that the process
of play ends under one of several circumstances:
1. both inventor and participants agree the game ends
In this case, the inventor of the game provides a rule
that defines the end of the game, and the participants
agree that this concludes the process, the other options
being to start the same game over or to shift to a new
game, in which case the participants remain within the
"magic circle."
2. the participants decide the game has ended
This can happen three ways:
i. the participants may select a stopping point not
dictated by the rules provided by the inventor
ii. in the case of a game which the players have
redefined, they may mutually define an endpoint
Unfoldings
iii. the players' sense of involvement and excitement
in the game may fade.
3. the discovery of an error or inconsistency in the rules
or the lack of an endpoint defined by the game's
inventor may "spoil the game"
Here play dissolves into confusion-and, due to the
extra-logical character of play, there is usually little
recourse in the rational assessment of the situation.
The magic of the game is usually preserved only if
some one of the participants steps in to provide a new
rule, and other participants accept both that person's
authority and the rule itself.
4. a participant may change or break a rule
Whether by error or by design, one participant's
deviation from the rules of the game may produce the
same dissolution as when the inventor's rubric fails.
Huizinga does not explictly treat the first three of these
outcomes, but he discusses this final case in some detail:
... as soon as the rules are transgressed the whole play-world
collapses. The game is over. The umpire's whistle breaks the
spell and sets "real" life going again.
The player who transgresses against the rules or ignores
them is a "spoil-sport". The spoil-sport is not the same as the
false player, the cheat; for the latter pretends to be playing the
game, and, on the face of it, still acknowledges the magic
circle. It is curious to note how much more lenient society is
to the cheat than to the spoil-sport. This is because the spoilsport shatters the play world itself.... He robs play of its
illusion, ... he is a coward and must be ejected. In the world
of high seriousness, too, the cheat and the hypocrite have
always had an easier time of it than the spoil-sports, here
called apostates, heretics, innovators, prophets, conscientious
objectors, etc. [22]
Huizinga's observations provide a fairly complete picture
of play 'in the abstract,' but I felt that the only way to fill
in missing elements and actually get a sense of the real
human process and dynamic of play was to actually
observe and engage in play. I needed both to see if
Huizinga's analyses of the characteristics of play were
borne out in action, and to test my comparisons of the
dynamic of play with that of intuition and creativity, so I
invented an observation game: The Play Experiment.
Characteristicsof Play
one of the first two or three objects they played with
(the physical qualities that relate playthings to
art-objects)
The Play Experiment
In order to obtain a better understanding of the actual
interactions of game players and their responses to rules
(particularly to shifting rules) and in order to collect a
sampling of opinions about the play/art/math questions
that interest me, I held an event called The Play
Experiment on the evening of February 12, 1992.
Approximately 35 people attended, mostly adults in their
20's and 30's, with two young participants (one age 2 and
one age 9), and with a few participants in the 40 to 65 age
range.
P L A Y
m
X
e
how players responded to rules during the
unstructured play session
e
how players responded to changing rules
The Experiment was not meant to be a carefully
controlled sociological or psychological research, but was
more a way to find out whether my ideas about the
responses of players to rules had any basis, and to discuss
the process of play with people who had just been in the
middle of it. The results are more anecdotal than
conclusive.
Session 1: Unstructured Play
"O
m
m
Z
The event lasted from 6:30 to a little after 9:30 in the
evening, and consisted of three sessions: 1 hour and 15
minutes of "Unstructured Play," about an hour of
"Structured Play," and a little less than an hour of
discussion. Participants filled out questionnaires during
the Unstructured Play session describing:
e
what characteristics attracted players to the first object
they played with
- what physical characteristics they remembered about
The purpose of the Unstructured Play session was to
allow the participants to select freely one or more objects
to play with. I wanted to see whether they were
influenced by, and later remembered, the physical
characteristics of the first object they played with or
whether familiarity was a stronger enticement than a toy
or game's physical attributes.
I set up the Experiment in the Exhibition Room of CAVS,
and provided a large number of toys and games-more,
in fact, than the number of Experiment participants. A
number of friends (see References at the end of this
chapter for acknowledgments) and I provided several
types of games and toys, almost all of which were the
sorts of things children or young adults would play with
indoors.
Unfoldings
A hopscotch pattern made by two friends and a play
sculpture that I designed called frameWORK greeted
participants as they followed the hallway leading to the
Exhibition Room. Inside the room the selection of toys
was arranged on about a dozen tables and on the floor
such that the more "physical" games and toys were close
to the door (where there would be a lot of activity and
movement anyway) and games or toys requiring
concentration or a lot of open space were toward the far
walls. Participants had to go to one of the farthest walls to
put down their coats and then backtrack to return to the
door.
Among the games and toys were:
e
wooden building blocks marked with symbols to indicate
that either the block is empty, contains a weight fixed at one
end, or contains a weight that can slide within the block
- a number of store-bought games and toys that either
my friends and I played with as children or that are
currently popular, and would be likely to be familiar
to my American middle-class contemporaries. A
partial list appears below (these names are
trademarked, and the owners of the trademarks
appear in the References at the end of this chapter):
Boggle, Chutes and Ladders, Clue, an Erector set, Etch-aSketch, Lego blocks, Liar's Dice, Mastermind, Memory, Mille
Bournes, Monopoly, Mousetrap, Othello, Pachisi, Perquacky,
Pictionary, Risk, Rubik's Cube, Scrabble, Slinky, Soma Cube,
Sorry, Spirograph, Stratego, Trivial Pursuit
several "classic" games and toys, some version of
which would be known to most Western children of
the "Baby Boom" era:
balloons, bubbles, building blocks, cards, checkers, chess,
dice, two or three dozen geometric "take-apart" puzzles,
jacks, jigsaw puzzles, juggling balls, kaleidoscopes, marbles,
two kinds of 3-D mazes to roll marbles through (one a
transparent plastic cube about 4 inches on a side, and the
other a construction toy), an electric model train, pick-up
sticks, 3-D tic-tac-toe, a half-dozen wire (or "tavern")
puzzles, tangrams, a stuffed teddy bear, tiddly-winks, yo-yos
e
a kaleidoscope with clear plastic shapes suspended between
polarized film layers and a cylindrical mirror surface
replacing the traditional angled flat mirrors
e
childhood
Autobridge, Booby Trap, Continuo, Lunar Probe, Reckon,
and geometric and logic games called Cornered and
Matchwitz
e
a number of variations of classic games that
introduced unfamiliar visual or tactile elements:
a battery-powered bubble gun that uses a mini-fan to blow
lots of bubbles out of the barrel when the player dips the
barrel into soap solution and pulls the trigger
a chess set with a soft, fuzzy playing board about 3 feet across
and plastic, sand-weighted pieces up to about 1 foot tall
several rather obscure store-bought gaines from my
several non-American games:
Owari and Mancala from Africa, Go from Japan,and
Husker-Du from Holland
e
two or three store-bought American and European
games and toys that have been produced within the
past several years, but would likely not be familiar to
the majority of the participants. A partial list (with
simplified rules) appears below:
Characteristicsof Play
Abalone: a two-player game in which the players take turns
pushing groups of one, two, or three marbles across a board
and try to push the opponent's marbles off the board. The
first player to eject six of the opponent's marbles is the
winner.
characters may decide to help out the farmer, or they may
decide to be as destructive as possible to ruin the farm.
Gravity Graph: a drawing toy consisting of a felt-tip pen
fixed vertically above a drawing surface mounted on a
swinging pendulum.
Hoomdorms: a pair of pneumatic 'robots.' The player pumps
air into the robot using a small hand pump, then removes the
pump and turns a switch. The robot jumps or flexes its way
across the floor for about 15 feet before its air supply runs
out.
Jenga (or Ta-Ka-Radi): a two-or-more-player game in which
small rectangular blocks are stacked in layers. Each layer
contains three blocks, all oriented the same way, separated by
a slight space. Each layer is oriented at right angles to the
layer below. Players take turns using one hand to pull out a
single piece from some layer other than the top one and then
add that piece to the top layer (keeping the same stacking
rule). The player who knocks the stack over while pulling out
a piece loses, and must re-stack the pieces for the next game.
Novi: a one-, two-, or several-player game in which the
players take turns laying down tiles that have black-andwhite patterns (the pattern on each tile is based on a 3x3
square grid) and try to create pathways and patterns.
Stack Challenge: a one-player hand-held electronic game
modelled on the arcade and computer game "Tetris." Pieces
composed of four squares in all possible edge-connected
configurations drop from the top of the screen, and the player
tries to rotate and move them in order to completely fill the
rows they fall into at the bottom of the screen. Completed
rows disappear, leaving room for more pieces to drop from
the top. The game ends when there is no more room for
pieces to drop because every row is incompletely filled.
Wabbit Wampage: a several-player role-playing game in
which players act out the part of rabbits on a farm. The rabbit
Still from the Play Experiment videotape shot by Dan Spikol
In the discussion at the end of the evening, a number of
people observed that almost no one was willing to start a
game that they knew would either take a lot of time or a
lot of concentration, or that seemed more "serious" than
playful. The best example of this was that no one played
chess during the entire evening, people agreed in the
discussion that chess has connotations of something more
complicated and confrontational than most games
(someone said "chess isn't a game, it's an obsession").
Unfoldings
However, several people played other games on the
chessboard-but only on the fuzzy chessboard. The handcarved wooden chessboard and chess pieces from Poland
were never touched. The physical aspects of the fuzzy
board and its pieces drew participants in-it was inviting
as an object, and so people treated the elements of the
chess game as toys, learning or inventing ways of playing
with them that did not have the negative connotations of
the game of chess.
The games and toys that were in use nearly continuously
throughout the evening were the marble raceway
construction toy, the bubble gun, the juggling balls, the
teddy bear, the geometric wooden puzzles Stu Coffin
designed, model train, and the Booby Trap game. Other
games and toys that were played with a lot were Abalone
game, the "tavern" wire puzzles, the Gravity Graph and
the Spirograph, the fuzzy chessboard (on which Marta
taught a Slovenian game and Pam Rockwell and I
invented a game based on checkers), the Boggle game,
and the weighted blocks. The following games and toys
were played with at least once: the backgammon set, the
go set, the balloons, the jacks, the Hoomdorms, the Jenga
game, Stack Challenge, Tiddly Winks, Lunar Probe,
Chutes and Ladders, Mastermind, the 3-D tic-tac-toe, the
Etch-a-Sketch, and the hopscotch (which, curiously
enough, was "played" a lot by people who came into the
Center in the week or two following the Experiment).
Session 2: Structured Play
After participants had been playing for a little over an
hour, I went around the room to the various groups of
players who were involved in games, and to one group
playing with a toy, and imposed a change. I gave each
group a choice: either they could make up a new rule for
the game they were playing (or for whatever game they
played with thereafter), or I would create a new rule for
them. The major groups responded as follows:
* the group of five people playing Boggle allowed me to
impose a rule, which was that they were allowed to
select one letter cube to skip over in word, so long as
they could get to it with the usual connection rules
(adjacent to the previous and next letters in the word
either vertically, horizontally, or diagonally)
* the group playing Stratego allowed me to impose a
rule, which was that a player could move one of the
opponent's pieces, but then had to make at least five
normal moves before doing so again.
e
the group playing with the marble raceway
construction toy allowed me to impose a rule, which
was that they had to find a way to make a three-way
path for a marble to follow at some position in the
structure
e
the group playing Booby Trap decided to make up
their own new rule, which was that each player had to
simultaneously remove two pieces, one with each
hand
My intent here was to find out how the groups responded
to the entire Experiment as a kind of meta-game, and
whether they accepted my invitation to play by the rules I
invented for the meta-game, or whether I was taken as a
'spoil-sport.'
Characteristicsof Play
What was most interesting was what happened after I
walked away from each of these groups. The Boggle
players decided that they were not happy with the new
rule I had created, and asked my permission to abolish
that rule and make up a new rule of their own. The
Stratego players did not use the rule for a long time, then
one of the players finally used it "when it would cause the
most damage." The group playing with the marble
raceway decided to reinterpret the rule, playing with the
semantics of the rule statement to change its meaning.
The Booby Trap players discovered that their new rule
made the game more interesting, and used it consistently
thereafter.
The responses reminded me of the various ways that
religious sects interpret the words of the gods. There are
those who don't like what the gods have ordained who
try to bargain with the gods to change the
commandments. There are those who don't like the
commandments but do not petition or pray for a change
of the laws, and who live within the letter of the law, but
transform its meaning to suit their preferences. There are
those who accept the commandment only when it suits
their purposes, and there are those who accept the
commandments as the guide for their behavior.
Interestingly, no one in the group admitted to simply
ignoring the 'commandments' altogether.
e
the difference between a toy and a game
e
players' responses to the physical and to the
conceptual characteristics of the games and toys
" the difference between a toy and a sculpture
e
players' responses to the initial rules of the games, and
to the imposition of the rule change-both their
response to me instituting the change, and how they
actually played thereafter (I described this above)
e
Huizinga's quote regarding the difference between the
spoil-sport and the cheat, and the difference in
society's response to these two archetypes
e
whether I, as the Master Gamer for the evening, took
on either the role of spoil-sport or cheat by changing
the rules
Toy vs. game:
The Players' definitions of these were fairly similar to my
own.Players defined a game as: goal-oriented; something
you can win; having a path, meaning a definite end-state
and a well-defined way to try to reach that state (it may
not always happen that you reach it); having some
evaluation system, such as scoring and points.
Session 3: Discussing Play
A point that several players stressed is that the rules ARE
the game-if you change the rules, you're no longer
playing the same game.
After about an hour of structured (or perhaps I should
have called it "re-structured") play, everyone gathered
around the central table in the Exhibition Room, and we
talked about several topics:
Players defined a toy as: something you can fantasize
about rather than having to play by the rules; an object
with socially defined (rather than written or codified)
rules; anything where, when you reach an apparent end,
Unfoldings
as when you've used up all the blocks you're building
with, you feel free to decide what to do next: "you get to
knock it down" and start again, "so you're not really
done, you get to do it some more."
Response to physical aspects of games and toys
Participants thought that they were generally quite aware
of the physical characteristics of the games, though I
found that most people's list of physical characteristics of
toys were quite incomplete. What was quite clear is that
the physical characteristics are a strong influence, even
where players don't remember them clearly.
One participant mentioned that he prefers playing
solitaire with real cards to playing in on a computer
because he likes the way real cards feel.
One player took exception to the statement by another
player that "the rules are the game, and the stuff that you
play with is just the stuff that you use to make the rules
work properly." He pointed out that the rules and the
"stuff" of
the game do have to match, or at least should
not conflict with each other in order to make the game
fun. He explained:
In Tiddly-Winks, you have a big 'tiddly' and a little 'wink.'
Well, we switched it: we winked the tiddles and boinked the
big things. Well, you were saying the stuff was arbitrary, but
it dictated what worked and what didn't work very well.
This same player said he is usually very much affected by
both the conceptual aspects of a game, i.e. rules, strategy,
symbolism, and the physical aspects, i.e. the way the
game looks the way the pieces feel, the way they move,
the patterns they make. He is generally aware of the
physical qualities as sculptural rather than toy-like: he is
aware of the physical characteristics but does not become
distracted by the possibilities those suggest.
On the videotape I watched one player get very absorbed
in experimenting with the physical qualities of one of the
pneumatic Hoomdorm toys. She exclaimed "Ilove this! I
love this pump!" (the pump went with the toys); she
carefully tested the feel of the moving legs against her
hand; she compared the way the toy responded on the
rug to the way it responded on the linoleum hallway
floor; she experimented with the amount of air it took to
get the toy to move and how it responded when it was
running out of air, and whether the switch on the side
changed the response. All of these are ways of figuring
out the intrinsic rules of the object, of responding to it, as
opposed to trying to impose rules, trying to make the
object respond. This player happened to report on this toy
in the "Physical Aspects" section of the questionnaire,
and her memory of the colors, shapes, sounds, and
materials was one of the two or three most complete lists
compared to all the respondents.
Toy vs. Sculpture
The majority of the players' comments here were pretty
straightforward: they said it's a sculpture if you only get
to look at it and a toy if you get to play with it. Thus toys
displayed in museum cases are sculptures (though that
was not their original nature).
One player mentioned the aspect of time in the difference,
saying "statues are static." Thus, like Huizinga, this
player associates action with play, and denies "toy-ness"
to still objects.
Characteristicsof Play
Another participant stated that a given object can be
either a sculpture or a toy (or puzzle) depending on how
the viewer responds. If they "appreciate" the shape and
the aesthetics, and if they "leave it alone," then it's a
sculpture.
Someone else countered, using the magnetized
Rhomblocks as an example, that it can still be a sculpture
and be moved around and rearranged. They said it's
more toy-like when "you're rearranging it for the point of
rearranging it-I can stick this piece against that piece
and the magnets make it stick-I would call that
experimentation versus 'directed' building."
One very interesting comment was one player's assertion
that finding the rules of a shape is the equivalent of
toying, and building according to rules and strategy is
sculpting. This differs markedly from my own definitions,
and has a curious implication (which the speaker may not
have thought about) that it makes sculpting into a logical
activity rather than an intuitive one-you should, by this
definition, be able to program a computer to do it if you
can state the rules and the strategy completely enough.
Spoil-Sports
In at least one situation, a player who looked at Booby
Trap as a game objected when another player treated it as
a toy. The first player wanted to know what the rules were
"so he could play." The second player treated the objects
as a toy: she felt free to invent her own rules for playing
with the object, which, in this case, meant experimenting
with and enjoying one of the physical characteristics of
the object-the rapid, jerky motion of the spring-loaded
bar.
Neither Huizinga nor I had considered the fine points of
the interaction of player's whose concept of the object of
play differed. For the player who expects the object to be a
game, especially a game whose rules the player is just
learning, the toy-player is an irritant, a usurper of
authority, clearly not a collaborator in the establishment
of order. The toy-player does not intend to destroy the
magic circle, merely to adjust its boundaries, However,
beyond a certain point, those who want the boundaries to
be narrower will label the irritant a spoil-sport.
What interested me is the leeway the toy-player has for
experimentation.This may be one of the factors that
causes experimenters and inventors in the plastic arts to
find their works greeted with the response "That's NOT
ART." One of the "rules" in art, simplistically put, is that
part of the point is to achieve certain effects through
application of a set of visual media and methods to be
experienced by a viewer. Another of the rules is that one
must invent: repeating one's own work too many times is
frowned upon within the artistic community as banal,
and repeating someone else's work without modification
is termed forgery. The acceptable effects, applications,
and media are all historically and socially defined within
the art-world. The result is that an artist who "invents" a
new effect, application, medium, or method, or
appropriates one from some other discipline, has an
oddly narrow boundary within which to innovate. If that
artist steps too far outside the standards within the artworld, the result is expulsion, excommunication by those
still within the tradition. The paradox of the art world is
the unspoken credo "Create, but don't get too creative
about it."
Unfoldings
Cheaters
Responses to the Spoil-Sport and the Cheat
The definitions the players gave for cheating were:
"deciding the rules don't apply to me," "changing the
rules without telling the other person," "not telling a new
player all of the rules, especially telling them only when
it's to your advantage and not to theirs."
A player pointed out that the severity of treatment of the
spoil-sport and the cheat depends somewhat on the
context. In tournament play, the spoil-sport is just
ignored, and it's the cheat who receives harsher
treatment.
Rule-Changing
Interestingly, none of the players saw my role in the
evening as that of a spoil-sport or cheat. They did
describe me as a meddler, a capricious higher authority
(but one that they did try to appease), and as the inventor
of a kind of meta-game the rules of which they had
accepted by coming to the event in the first place.
The complete description of the results of the rule
changes appear on page 28.
I DIDNT WN T PWZ MS
@\OTK GNAE: IN TV
Contests and Tests of Skill
Though I did not explicitly ask the players about goals
and about the relationship between play and the sense of
achievement, the subject came up once or twice, as
mentioned above. The videotape captured several short
competitions and a couple of tests of skill that the players
created.
C1987 Unbb,Pr
yBW
Calvin and Hobbes, by Bill Watterson
In one vignette, the 2-year-old (whose vocabulary still
consisted of single words only his parents could
understand) created a test of skill for himself. He was
trying to place one of the marble raceway sections at the
top of a tower nearly as high as his shoulders. Since he
was holding the piece upside down, it wouldn't fit. His
father gently repositioned the piece in his hand, and
Characteristicsof Play
another player steadied the tower. The child ignored
everything around him, including encouragement from
the person steadying the tower until the piece dropped in,
and stayed where it was when he took a step back and
paused. Upon seeing that the tower stayed up, the child
exclaimed "Yay!" and clapped his hands and reached for
another piece. I found this an interesting demonstration
of the idea that play is truly fundamental, that the desire
to test oneself is ingrained by the age of two (a still image
from this sequence appears on page 27).
One player mentioned selecting a first toy because it
reminded her of a different, more goal-oriented puzzle
(Rubik's Cube), but that the less goal-oriented version
(colored cubes connected by elastics that let you twist the
whole toy out of the cube shape) left the player with the
option of ignoring the goal-this player immediately
recognized both the contest or goal-potential of the
object-as-game, which Huizinga describes in some detail,
as well as the creative potential of the object-as-toy that I
had posited.
Another episode on the video shows a group of four
people all playing with small wire and geometric puzzles.
They are gathered in a loose circle, and none of them are
talking, but they occasionally look over at each other's
progress. One player gets his puzzle apart, and silently
holds up the pieces: the obvious implication is that he has
won. The others all look over, without pausing in their
own tinkering, and one of them nods. They all go back to
working on the puzzles. The group has, without any
discussion, established their activity as a being both
individual and social.
There were several things I noticed about the group's
response to the physical characteristics of the games. The
first was that, where I had provided two versions of a toy
that differed in tactile quality, the softer one was used and
the harder one was untouched, for example, the two
chessboards and the two stuffed animals. However,
during the discussion period, no one seemed able to talk
about why that was so. From observing the participants, I
conclude that the softer game or toy provided more
possibilities to the player, made them feel a little freer to
focus on the potential of the object rather than on the rules
associated with it.
Analysis of Questionnaire Responses
Of the 35 or so participants, seven or eight did not stay for
the whole event, and, of the ones who stayed, 22 filled out
questionnaires.
The most common reason people chose a particular game
or toy at the beginning of the evening was familiarity.
Nine participants gave this as one of their reasons for
selecting the first toy, and many of those mentioned that
their first response was nostalgia for the times they
played with the toy or game in the past.
Unfoldings
The strongest secondary reasons for selecting the first
game were visual:
Reason
The responses to the section of the questionnaire that
dealt with rules were somewhat curious in that no one
admitted to cheating or to having anyone else cheat:
# of times
checked
The game was unfamiliar, but looked
interesting
7
Liked the shapes
6
Played with the first thing you saw
6
Liked the textures or materials
4
Liked the colors
3
The social aspects were, somewhat to my surprise, down
at the very bottom of the list:
Reason
# of times
checked
The players of the game added or
invented a new rule
8
Players knew different versions of a
game
6
Players disagreed about game rules
5
Rules provided with the game were
incomplete or unclear
4
# of times
checked
Players of the game decided to get
rid of or ignore a rule
A friend asked you to play
2
You or someone else "cheated"
A stranger asked you to play
1
Watching someone else play with the game
got you interested
1
Reason
You had heard of the game1
0
There was one instance caught on videotape where one
player accused another of cheating at backgammon by
not explaining all the rules, and allowing the novice
player to make mistakes.
Conclusions
In the main, I found that my hypotheses were borne out
by the events in the Experiment. There were a number of
issues that I found myself still curious about, and I would
have liked to hold additional experiments, particularly
Characteristicsof Play
one focused on creative play and on responses to changes
of visual and physical rules (I had planned to call that one
The Illusion Experiment).
Among the issues raised but not answered were:
* ways of testing the proposition that building
intuitively is toying and building according to rules is
sculpting
" what factors affect the leeway a player has to be
inventive without being labelled a spoil-sport, and
how that relates to the 'outsider' in art
- how to manipulate an image or object to cause
viewers to see it first as toylike and second as
sculptural, or vice versa
All of these are interesting questions, but they will have to
be deferred for now.
Unfoldings
Chapter References
[18] The Intimate World of Alexander Calder by Marchesseau,
p. 152.
(Please see the Bibliography for complete publication
information for book citations.)
[1]
Homo Ludens: A study of the play element in culture by
Johan
[19] The Intimate World of Alexander Calderby Marchesseau,
pp. 24-5.
Huizinga, p. 4.
[20] Agam by Frank Popper, pp. 139-140.
[2]
Ibid, p. 211
[21] Principlesof Neo-PlasticArt, by van Doesburg, p. 39.
[3]
Ibid, pp. 7-8
[22] Homo Ludens. pp. 11-12.
[4]
Ibid, pp. 8-9.
[5]
Ibid, pp. 8.
[6]
Principlesof Neo-PlasticArt by Th6o van Doesburg, p. 5.
[7]
Ibid, p. 29.
[8]
Homo Ludens, pp. 9-10.
[9]
Ibid, p. 51.
[23] I wish to thank the following people who graciously
lent toys and/or taught games for the Play
Experiment: Jeff Carter, Dr. Willard Johnson and Dr.
Vivian Johnson (my parents), Peter Atlas, Pam and
Dennis Rockwell, Jennifer Sa win and Jim Herndon,
Beth Kevles, Stewart Coffin, Josh Boughey, Chaya
and Hillel Shahan-Bronberg, Otto Piene and
Elizabeth Goldring, Gregory Haun, Joe Gaudreau,
and Zora Jones Rizzi and Diane Willow, who made
the terrific hopscotch in the front hallway for me.
Many thanks to Dan Spikol for videotaping the
event.
[10] The Intimate World of Alexander Calderby Marchesseau,
p. 29.
[11] History of Art by Janson, pp. 660-61.
[12] Bauhaus by Frank Whitford, p. 12.
[13] Fluxus, by Phillpot &Hendriks, frontspiece.
[14] The Intimate World of Alexander Calder by Marchesseau,
p. 31.
[15] Calder's Universe by Lipman, p. 81.
[16] Homo Ludens, p. 10.
[17] The House at Pooh Cornerby A. A. Milne, pp. 94-5.
The following companies own copyrights on the
games listed below:
Abalone Games Corporation: Abalone
Discovery Toys: Marbleworks
Gabriel Industries: Othello
Ideal: Mousetrap
Invicta Plastics Ltd: Mastermind
Leisure Dynamics: Perquackey
Matchbox International, Ltd: Rubik's Fifteen
Milton Bradley: Chutes and Ladders, Stratego,
Characteristicsof Play
Tiddly-Winks
Ohio Art: Etch-a-Sketch
OrDa Industries: Mini Gravity Graph
Orphyte, Inc: Wabbit Wampage
Parker Brothers: Autobridge, Clue, Mille Bornes,
Monopoly, Option, Risk, Sorry
Pictionary Inc: Pictionary
The R/L Group: Noiv
Rex Games: Tangoes
Robbert de la Rive Box: Scope
Rockland Group: Gravity Blox
Selchow & Righter: Parcheesi, Scrabble; Trivial
Pursuit
Seven Towns Ltd: Rubik's Cube
Tomy: Hoomdorm
Figure Credits
Page 13: "Haiti, 1950" ©1991 George Rodger, printed by
Editions du D6sastre, Paris.
Page 16: "Dali Atomicus" Photograph by Philippe
Halsman, 1948 © Yvonne Halsman, printed by
Fotofolio, NY.
Page 17: "Rapenburgerstraat"@ Dolf Kruger 1956,
printed by Art Unlimited, Amsterdam.
Page 17: Firemen's dinner for Brancusi, from The Intimate
World of Alexander Calder, p. 29.
Page 20: Christopher Robin knighting Pooh, and Page 21:
A game of Poohsticks, from Ernest H. Shepard's
drawings for The House at Pooh Cornerby A. A. Milne.
Page 22: Dog, by Alexander Calder, 1940, page 85 of The
Intimate World of Alexander Calder by Marchesseau.
Page 22: Bull's Head by Picasso, 1943, page 9 of Historyof Art
by Janson.
Page 32: Calvin and Hobbes, by Bill Watterson from the
Bostion Sunday Globe, Jan 5, 1992.
Unfoldings
The Role of Play in the Visual Arts
There is a major point where I disagree with Huizinga's
treatise. When he comes to the question of the
relationship between play and art, he claims that:
Turning from poetry, music and dancing to the plastic arts we
find the connections with play becoming less obvious....
The very fact of their being bound to matter and to the
limitations of form inherent in it, is enough to forbid them
absolutely free play and deny them that flight into the
ethereal spaces open to music and poetry. [1]
Huizinga bases this view on three observations. First, he
claims that, even if the inspiration of a work involved
play, the labor required to make the work is just that:
labor, not play, and thus "the play-element is to all
appearances lacking in the execution of a work of plastic
art." [2]
Second, he looks upon the plastic arts as static, lacking
what he calls "visible action" within the works
themselves, and lacking the quality of unfolding in time
before the observer, as in dance and music, so that:
The absence of any public action within which the work of
plastic art comes to life and is enjoyed would seem to leave
no room for the play-factor. [31
Huizinga's third claim is that, in a work of plastic art:
the very nature of the thing. . . is determined to a large extent
by its practical purpose-and this is in no way dependent on
aesthetic impulse. The man who is commissioned to make
something is faced with a serious and responsible task: any
idea of play is out of place. [4]
The only areas where Huizinga will grant the infiltration
of play into art are the cases where art serves the purposes
of ritual, and where the creation of artwork is made into a
form of contest.
I take exception to all three of Huizinga's arguments
against the existence of a play-element in art, and offer the
following observations and references.
Regarding Huizinga's notion of the nature of plastic
artworks, I strongly disagree that there is or should be a
"practical purpose" for most works that can be called fine
art: the fine artist does not take brush in hand merely to
relieve the starkness of a blank wall. I also disagree that
the nature of the work is entirely dictated by such
purpose even where it does exist: even when the artist is
commissioned by someone whose goal is merely to cover
the wall, the artist must still come up with an image. This
Unfoldings
is a creative rather than a practical endeavor. Where
practical purpose does dictate the character of the work, I
believe that is the major factor that transforms the work
into an example of design, craft, or illustration rather than
art.
Regarding the making of an artwork, I demonstrated in
the previous chapter the strong similarity between the
creative process and play by drawing parallels to
Huizinga's four characteristics of play. I showed that:
*
intuitive and creative actions are voluntary and
cannot be forced
e
creative labor often distances the artist psychically
from the concerns of daily life for a while
e
artists have traditionally worked in studios physically
removed from living and working space, but creative
work in public has a similar character to play in public
e
the discovery of order within form and the imposition
of order on form are the essence of the creative process
in the visual arts.
True, making art is not always playful-some of it is
exactly as Huizinga describes: it is physical labor. But the
artist must keep gauging the progress of the piece against
intuition and aesthetic judgement, so the play-element is
most certainly apparent again and again in the midst of
the work.
moment, whether or not that actually dictates the nature
of the work), if the object's purpose is to be a toy, a simple
connection can be made between the plastic arts and play
Among toys designed by artists, perhaps the most famous
example is Calder's Circus (a toy that ended up
occupying more than five trunks). Before he began the
famous Circus itself, Calder made several others,
including a small circus he made for himself at the age of
seven. In addition to making animals and figures from
bits of wire, wood, and whatever, Calder drew sketches of
the animals at New York's Bronx and Central Park Zoos,
and of the performers and trained animals at circuses
during the early 1920s. Rather than being an object
designed for a purpose, the circus was an extension of
Calder's observation of and love of animal and human
forms and actions.
Calder made numerous toys and "amusements" for his
family and friends: "nose masks," fantasy eyeglasses,
pull-toys, doll houses, and a seemingly endless collection
of animals and figures. Though he received a couple of
commissions to make toys and circuses, he didn't find the
majority of toy companies receptive to his efforts:
William Hayter recalled, "This was when Sandy began
making toys (1927). I can still remember how naively
astonished he was when the toy manufacturers were not
interested in his ingenious toys: they amused the children
and ourselves so much! I guess he didn't realize that toys are
manufactured by people who claim to understand what the
parents (who pay) think their children will like." [5]
Play Sculptures
Some would argue that these aren't artworks. Certainly
Re-examining the claim that an artistic object's nature
derives from its practical purpose (ignoring, for the
many of Calder's creations were objects that would, by
many definitions, be called craftworks-his jewelry and
The Role of Play in the Visual Arts
kitchen utensils, for example. However, the object's utility
wasn't usually the main reason for making it, nor for
making it in a particular way: they were made in a spirit
of aesthetic play, creativity and invention. Calder himself
recognized that naming his creations could cause
controversy:
Calder commented about the toys he made, "They call me
a 'playboy' you know. I want to make things that are fun
to look at, that have no propaganda value whatsoever."
[7] To his grandniece, Nanette, he wrote: "Above all, I feel
art should be happy and not lugubrious." [8]
Calder deliberately uses the word 'work' instead of 'art,' and
he usually calls individual pieces 'objects' because "then a
guy can't come along and say, no, those aren't sculptures. It
washes my hands of having to defend them." [61
Chess Set designed by Bauhaus teacher Josef Hartwig, 1924
Calder roaringwith the Circus lion, 1971
Calder is certainly not the only artist to make toys. The
chess set has been a favorite art-toy, with examples
produced by members of many different art movements.
There is Josef Hartwig's Bauhaus chess set whose pieces'
shapes indicate the way that they move, instead of
resembling a royal retinue. Teeny and Marcel Duchamp
made a chess board, for which Calder made the pawns
Unfoldings
(out of checkers and bolts) and the box, and on which
Man Ray painted the text:
Le Roi est Amoi-la Reine est la tiennela tour est un four-le jou est comme vousle cavalier deraille-le Pion fait l'espion
comme toutes canaille.
Fait de toutes pieces pour Teeny et Marcel
Man Ray 1964 [91
[My own loose translation:
The King is mine, the Queen is yours,
the Castle's gone and failed.
The game's exactly like we are,
the Knight has been derailed.
The Pawns all play at spying
like the rabble that we railed.]
Teeny and Marcel Duchamp's chess set
Several of the artists of the Fluxus movement of the 60's
and 70's, founded by George Maciunas, produced games
which Maciunas mailed out in art-for-the-masses Fluxus
'magazines.' These magazines were small wooden crates,
stamped with the word 'FLUXUS' and containing a
jumble of texts and objects. 1
The artist Takako Saito seems to have been the Fluxus
artist in charge of chess sets. She made at least nine
FLUXCHESS sets between about 1965 and 1973. Many of
The Role of Play in the Visual Arts
them had the goal of making the players identify the
pieces by some sense other than sight. They included:
e
nut and bolt chess
A rather crude stepped wooden board and pieces
made of painted bolts.
e
jewel chess
Pieces consisted of jewelry in small plastic boxes
e
grinder chess
This set had pieces made of machinist's grinding
wheels and brushes (pictured below).
Saito's grinding-wheelchess set
* smell chess
The pieces were clear vials containing the liquid
essence of various perfumes. The pieces could only be
told apart by their smell
* sound chess
1. It's interesting to note that the original meaning
of the word 'magazine' is storehouse or a box of
munitions, so Fluxus boxes are closer to being
'magazines' than the glossy paper objects we now
call by that name. [10]
The pieces were small plastic boxes containing small
objects which, which shook, made different sounds.
The boxes were all identical, and could be opened to
view the contents
Unfoldings
* weight chess
The pieces were small plastic boxes of various weights
- spice chess
The pieces were corked test tubes containing various
spices. From the top all the corks were identical
Yoko Ono made a set that really did test the line between
sculpture and toy: an all-white set on an all-white board
which she titled Play it by Trust.
The Fluxus group produced lots of other toys as well,
including George Brecht's games, puzzles, and decks of
cards. These were games with a twist-for example, there
was a deck of cards in which all 52 of them were the King
of Spades, and there was a box containing a cup, a coil of
wire, a pen, a chesspiece, an eggshell, various other small
objects, and a card reading "Spell your name with these
objects." These games couldn't be played without the
active, inventive participation of the player, who was left
to make most of the decisions about the rules to the
games.
George Maciunas, the founder (or perhaps he would say
the instigator) of Fluxus, felt that toys and games were at
the heart of the Fluxus attitude, in contrast with the
attitude of the established art world. He wrote the
following text for the Fluxus Broadside Manifesto in
19652:
2. I did not find an English-language copy of this text until
May 7th. This quote is my own translation from the French.
Art:
To justify his professional status as an elite societal parasite,
the artist must demonstrate that he is indispensable and
exclusive, that his audience depends on him, that only artists
can make art.
In consequence, art must seem complex, pretentious,
profound, serious, intellectual, inspired, adroit, theatrical,
significant. It must seem to have commercial value in order to
become, for the artist, a source of income. To increase its
value (and therefore the income to the artist and the profit to
the patrons), art must seem rare, available in limited
quantities, and therefore accessible only to the elite and to
large institutions.
The Art/Game of Fluxus:
To establish his non-professional status in society, the artist
must demonstrate that he is neither indispensable nor
exclusive, that his audience can be self-sufficient, that
everything can be art, that anyone can make art.
In consequence, the art/game must be simple, amusing,
without pretention, preoccupied with insignificant things,
neither demanding specific abilities nor uncountable
repetitions, and having no commercial or institutional value.
The value of the art/game will be reduced by being available
in unlimited quantities, mass produced to be accessible to
everyone and eventually produced by everyone. The art/
game of Fluxus is an "arrire-garde" without either
pretention or desire to challenge the "avant-garde" in the
fight for supremacy. It contents itself with being
monostructural, non-theatrical, with the character of natural,
simple facts, of games, of gags. It's a mixture of vaudeville,
gag, child's game, Spike Jones, and Duchamp. [11]
The Fluxus artists were aware that toys and games have a
special power to engage, to change an observer into a
participant, and that the game was therefore a tool that
could be used in the context of art to change a viewer-ofart into a creator-of-art, by enticing the observer to join
The Role of Play in the Visual Arts
the art-maker's magic circle, and by sparking a creative
response.
The rest of this chapter constitutes a brief treatment of a
number of artistic movements that focused on the kind of
spatial play that Huizinga claims doesn't exist.
Space-play
Trompe l'Oeil and Anamorphosis
Going beyond art-toys, there exists a deeper connection
between art and play. Huizinga claims that the plastic arts
cannot incorporate play because they are tied to matter
and its limitations, but it is precisely when artists make
their works transcend these limitations that play enters
the plastic arts.
It is here that mathematics begins to enter into the game
as well, for, in working with the inherent limitations of
space and form, artists often needed either to explore the
existing abstract "languages" in which the laws of those
limitations are formulated or to develop such abstract
languages themselves. A number of artists were also
influenced by developments in other disciplines that
proposed connections among science, mathematics, and
spirituality, and made visual references to these ideas.
The evasions of spatial limitations in the plastic arts take
various forms:
* twisting spatial rules in both subtle and overt ways
* celebrating the 'limitations of form' by treating pure
form as a subject
- making the eye see something more than the actual
elements of the image
e
creating an image that cannot be experienced in reality, defying everyday experience and physical laws
Many Renaissance painters sought to match their works
to the eye's expectations, attempting to master the
shaping of a form through light and shadow, and to
understand and follow the rules of projective geometry,
and thus create scenes that appeared to present objects as
they would actually appear in space. The mathematics of
perspective had been developed centuries early by
Euclid, Ptolemy, Galen, and Alhazen. The beginning of
success in the Renaissance endeavor came in the works of
Brunelleschi and Masaccio around 1425, who were among
the first painters of the modern era to accurately depict a
scene with a single vanishing point. Brunelleschi
succeeded in painting the Baptistry of Florence in
accurate one-point perspective using a scheme in which,
with his back to the building, he painted what he saw in a
mirror aimed at the Baptistry. [12]
Unfoldings
Painters of the 17th and 18th centuries revived
investigation into geometric techniques, exploring twopoint perspective to give their images greater realism. A
small number of painters carried the exploration of
projective technique to the extreme. 17th century painters
of the School of Delft, one of the best known being Samuel
van Hoogstraten, created perspective cabinets, painted on
the inside with scenes that appeared in realistic
proportion only when viewed through a special peephole. The cabinets were a kind of play on the tradition of
the "perspective box" spatial division in painting, in
which all scenes, including landscapes, were depicted as
they would appear if built as a scene inside a box or stage.
113]
Some artists painted objects that came into view when the
viewer looked at the wall or canvas obliquely and from a
distance, as in Holbein the Younger's memento mori-the
skull that appears when one looks obliquely at the
canvass-in his painting The Ambassadors. A number of
European artists even produced images that were, in
essence, visual puns, simultaneously portraying a lush
landscape when one looked at the canvas face-on and one
or more portraits in the oblique view.
The images shown here and on the following page are
from the catalog of a 1975 tour of anamorphic paintings
and sculptures collected from around the world. The
notes for Schon's "picture puzzle," shown below, state:
This type of witty representation proves to be an everrecurring one. The analogy between the man relieving
himself and the whale that spat out Jonah is a truly original
interpretation of this Biblical event. [14]
Erhard Schun. Picture Puzzle: What do you See? ("Was Siechst du?") 1538
-- ----------------------
- - -------ftiv-,
AARCO"
-I
C.
----------
The Role of Play in the Visual Arts
In China, Turkey, and France, a few 17th artists produced
another sort of anamorphic image that could be
interpreted properly only when reflected in conical,
cylindrical or pyramidal mirrors.
Thus what had begun in the 1400's as a quest to conform
to the exacting rules of projection became a kind of play
on those very rules, demonstrating not only mastery in recreating a scene as it would appear to the eye, but in
manipulating the image and presenting scenes as they
would appear if the eye itself were quite different than it
is, able to see two views simultaneously or to see in all
directions at once.
Non-Objective Art and Concrete Art
The second evasion of spatial limitation is not an evasion
at all. It is the route taken by those who embrace the
mysterious power of abstract and of geometric form itself,
those who believe form and color alone to be potent
enough to incite a creative response from viewers used to
more figurative, representative images: artists such as Piet
Mondrian and Wassily Kandinsky.
Mondrian's goal was to generate a sense of equilibrium,
through what he perceived to be a lost connection to a
cosmic unity, by visual representations of a kind of "holy
mathematics:"
Crucifixion with Mary, John, and an Angel, c. 1640. Cylinder anamorphosis
with reflecting cylinder
The catalog notes for the crucifixion painting shown
above comment:
In the northern Netherlands, there were, as we have learned
from the perspective cabinets, many painters who were
particularly interested in optical phenomena-clearly a
congenial atmosphere in which anamorphoses could
originate. [15]
A mathematical system was for him not a tool but an artistic
solution to a formal problem-a solution that, however
paradoxical this may sound, had an intuitive origin...
. Like
many other Dutch artists of the early twentieth century, he
based his use of mathematics on a belief that there is a higher
reality, with a systematic logical structure, behind the natural
appearance of things. [16]
Kandinsky took as a guiding principle for his works the
representation of tension and conflict, "making the
spiritual visible in abstract forms and colors," and
achieving "spiritual renewal... by turning to the abstract,
the elemental." [17]
Unfoldings
illusory, more vague, more speculative than a plane or a line.
[18]
... and by Max Bill:
We call "concrete art" works of art which are created
according to a technique and laws which are entirely
appropriate to them, without taking external support from
experiential nature or from its transformation, that is to say,
without the intervention of a process of abstraction.
Concrete art is autonomous in its specificity, it is the
expression of the human spirit, destined for the human spirit,
and should possess that clarity and that perfection which one
expects from works of the human spirit.
It is by means of concrete painting and sculpture that those
achievements which permit visual perception materialize.
The instruments of this realization are color, space, light,
movement. In giving form to these elements, one creates new
realities. Abstract ideas which previously existed only in the
mind are made visible in a concrete form.
Concrete art, when it is true to itself, is the pure expression of
harmonious measure and law. It organizes systems and is
real and intellectual, anaturalist while being close to nature.
It tends toward the universal and yet cultivates the unique, it
rejects individuality, but for the benefit of the individual. [19]
Small Worlds VI by Wassily Kandinsky
This category includes those who called themselves
Concrete Artists as defined by Thdo van Doesburg:
concrete and not abstract painting, because nothing is more
concrete, more real than a line, a color, a surface. Are a
woman, a tree and a cow on a canvas concrete elements?
No-a woman, a tree and a cow are concrete in the natural
state, but in the state of painting they are more abstract, more
These artists were aware that the abstract elements they
chose as their material must be used carefully, avoiding
the creation of empty images. Kandinsky wrote:
If we begin at once to break the bonds which bind us to
nature, and devote ourselves purely to combinations of pure
color and abstract form, we shall produce works which are
mere decoration, which are suited to neckties or carpets.
Beauty of Form and Color is no sufficient aim by itself. [20]
These artists sought a visual route to the spiritual, a
means of sparking the creative response Huizinga
The Role of Play in the Visual Arts
ascribes to play situations: the sense of being transported,
distanced from animal needs and logical thought, and
participating, suddenly, in a transcendent order.
Variation 2 of "fifteen variationson a single theme"
Variation I Of "fifteen variations on a single theme" by Max Bill
Op Art and Spatial Ambiguity
The third form of space-play, making the eye appear to
see something more than the elements of an image, was
the method of a number of 19th and 20th century artists.
They explored the limitations of the eye's perception,
developing another kind of visual pun-they painted
images containing ambiguities that viewers saw as
shifting images. They explored color perception, learning
to make the beholders of their images see colors other
than the ones in the artist's palette. Particularly in the 20th
century, they also explored techniques for making the
figure-ground relationship and the perspective clues of
the image itself ambiguous, creating a sense of dynamic
variation and movement in static images.
Unfoldings
The early 20th century artists followed in the path of Josef
Albers and Victor Vasarely, who established what would
later be called Op Art. As with Mondrian and Kandinsky,
these artists described as their ultimate goal the
generation of a sense of transcendence and higher
awareness.
Describing a series of his black-and-white prints, Josef
Albers wrote:
These lithographs are built exclusively of horizontal and
vertical lines which are the most two-dimensional and
therefore the most non-spatial graphic elements.
These abstract compositions perform space and volume
illusions of multiple images, thereby inducing several
interpretations.
Receding directions are imaginary, appearing only through
related junctions of horizontals and verticals.
Movements are not confined to one direction only, but
interchange. Thus solid volume shifts to open space and
open space to volume. Masses moving at first to one side
may suddenly appear to be moving to the opposite side, or in
another direction.
Likewise, upward acts as downward, forward as backward,
and verticals function as horizontals. Parallels, horizontals or
verticals, produce sloping planes, empty spaces become
solid. Black lines produce gray tones, and, for sensitive eyes,
color.
Thus we cannot remain in a single viewpoint, we need more
for the sake of free vision. [21]
Much of Albers' writing and poetry expresses, in one way
or another, the idea that the possibility of ambiguity in
two dimensional imagery represents the possibility of,
and an incitement to, transcendent freedom of thought
and spiritual vision.
Vasarely believed that this special, shifting perception of
two-dimensional images could take the place of
iconography in communicating to his audience, and
would allow that communication to take place in the
intuitive realm rather than in the more limited realm of
perception. In his monograph on Vasarely, Werner Spies
explains:
[Vasarely's] world ... might be designated the iconography of
optical aggressiveness. This world lies between the art of
perception, which makes a theme out of the visibility of an
object, the intensity of its appearance in the field of
perception, and the art of apperception,which aims at bringing
about an understanding over and above pure perception....
Merleau-Ponty describes this reaction to an ambivalent
perceptual figure and points out that it is impossible to apply
learning or habit to such phenomena. [22]
The Role of Play in the Visual Arts
All of the artistic movements I have just described
playfully employ the rules of two-dimensional as
compositional tools for increasing the power of plastic
artworks to entice the viewer into an intuitive, creative
response to the work and from there, in the 20th century
movements, in any case, into a transcendent, spiritual
response to the deeper issues beyond the limits of the
image.
Time-play
In the midst of this exploration, a number of artists began
to consider the possibilities of adding actual and spiritual
dimension to their work, through visual exploration of
discoveries in the fields of physics and mathematics. The
very nature of space and time had been called into
question, and a number of artists felt that the conceptual
space and time of the elements of the plastic arts also
required scrutiny. Of the artists already discussed, Van
Doesburg in particular felt compelled to consider both
time and the spiritual realm as possible fourth
dimensions that must be expressed in art.
Vega by Vasarely, 1857
Vasarely's ideas have been further developed by such
artists as Bridget Riley, whose images, many of which are
built up of simple manipulations of simple patterns, are
completely baffling in their vertiginous effect.
The consideration of a fourth dimension and of time in art
is rather controversial, as attested to by Linda Dalrymple
Henderson's monumental treatise on the subject (The
Fourth Dimension and Non-Euclidean Geometry in Modern Art). Many
artists, and many observers of art, believe that, even in
what Huizinga would call a "static" painting or sculpture,
time is an essential element if only because the viewer
must experience the work through time, examining first
one part of the piece and then another. Some take the
more complex view that the viewer should be made to be
aware of time, that the work should embody
Unfoldings
characteristics of time just as it embodies characteristics of
space. Other artists do not accept this view, some feeling
that even if time can be made an element of painting that
it should not be allowed to enter-for example, Mondrian
was quite disturbed at Van Doesburg's proposition that:
an artist should take into consideration the new scientific
discovery [new in 1922 at least -CJ] that perception is
dependent on place and time: "As a result of the new
scientific and technical widening of vision, a new and
important problem has arisen in painting and sculpture
beside the problem of space: the problem of time." [23]
Hoek explains Mondrian's concern thus:
He was convinced that there existed one universal reality,
which was the same in all places and at all times. Because
things assume different aspects at different points in time,
mankind was, according to him, no longer aware of the
cosmic unity. Natural appearance, bound to place and time,
disguised reality. In order to create a purely abstract image of
the universal, it was necessary to do away with the aspect of
time in the presentation. [24]
But for those artists who do believe that time is and
should be an element of the plastic arts, time becomes
another creative means, another tool for eliciting a
creative response, and for achieving Huizinga's elusive
flight into ethereal spaces. These artists, by the very
nature of this incorporation of time, counter one of
Huizinga's arguments about the static quality, the lack of
"unfolding," he perceived in the plastic arts. Here, at last,
the complaint that the play-factor cannot operate in the
"absence of any public action within which the work of
plastic art comes to life and is enjoyed" is directly
countered (see page 39).
As Henderson shows, the element of time and theories of
space-time had a profound influence on many of the art
movements of the early 20th century, Dada, Cubism and
Surrealism in particular. I shall not attempt the impossible
and foolish task of distilling her excellent text into a few
paragraphs, but shall instead consider the effect the
incorporation of time had in one of the artistic trends I
have already introduced, and will describe the time-based
works of two artists whose work relates to my own.
Op Art and Temporal Ambiguity
One of the groups of artists to consider the time element
were much inspired by Vasarely. This was a group of a
half dozen young men, Fran ois Morellet and Vasarely's
son Yvaral among them, who called themselves Groupe
de Recherche d'Art Visuel (GRAV), and referred to
themselves as researchers rather than as artists, thereby
tying their activities in form as well as in subject to the
scientific community whose theories served as one
inspiration for their work.
The sections of the 1961 GRAV statement of purpose
describing the changes they desire to bring about in the
relationship between the artist and society bear
remarkable similarities to the Fluxus Art/Game
statement by Maciunas-one may well have been
influenced by the other. The section of the statement that
is relevant here describes the GRAV propositions for
changing the accepted relationship between the viewer's
eye and the artwork, in which the eye is merely a filter,
colored by non-visual preconceptions. GRAV desired to
eliminate all the intrinsic and traditional associations of
form, including those professed by classical art,
The Role of Play in the Visual Arts
naturalistic art, cubist art, abstract constructivist art,
concrete art, and action painting, and to eliminate what
they term arbitrary relationships among forms. The next
step they proposed was:
to shift the usual function of the eye (to gather knowledge
through forms and their relationships) toward a new visual
situation based only upon the limits of peripheral vision and
visual instability. To create a time-awareness based on the
relationship between the eye and the work transforming the
usual quality of time. [25]
This is quite a dramatic step-the implication being that,
in order to add the element of time to their works, it was
necessary to throw away the precepts of all prior artistic
movements, including precepts of movements that
purported already to have tried to eliminate naturalistic
and arbitrary formal relationships.
The paintings that the GRAV artists Stein, Sobrino,
Morellet, and Rossi produced owed much to Vasarely's
investigations of simultaneous contrast, moire-patterns,
and the vibratory effect of making slight changes in angle
and color in repetitions of simple forms. Le Parc's
plexiglas works added slight physical movements and the
resulting shimmer of reflected light to the collection of
tools intended to produce the desired "new visual
situation." Sobrino's plexiglas works sought to translate
the unstable visual effect of painted color combinations
into the realm of color combination in light, through the
interaction of color and transparency of layers of
geometric plexiglas shapes:
Each level loses its individual color-form personality in
combination with those on the other side of the work. The
movement of the spectator around the piece equally alters
and accentuates the play of these combinations. [26]
Yvaral's "plane-spaces" of criss-crossing cords of vinyl
and rubber on plexiglas frames combined the effects of
moire and relief, producing a sense of dizzying vibration
in a viewer standing still in front of the work, and
producing absolute vertigo as the viewer moves.
One important new factor here is the expectation that the
spectator will observe the piece while walking back and
forth, that the full effect of the work depends on the
viewer's experience of movement and time in a different
way than prior artworks. Yvaral's works, in particular, are
carefully calculated to make the observer perceive the
works as animated-but the trick is that what Yvaral has
actually done is animate the observer.
Kinetic Art: Mobiles and Transformables
The next category to consider is a subset of the field of
Kinetic Art. The meaning of the term 'kinetic' in relation
to art is extremely broad: depending on whose definition
one follows, it includes everything from the illusory
movement-effects of Op Art to the physical motion of
mechanical and motorized machine-sculptures by a large
variety of artists, including Naum Gabo, Lazlo MoholyNagy, Man Ray, and Jean Tinguely.
Some artists have managed to combine different kinetic
elements in a single work, as in Duchamp's 1925 Rotary
Demisphere and 1935 Rotoreliefs, in which the interactions of
patterns derived from concentric and eccentric circles
mounted on spinning bases produced effects of threedimensional spiraling. Duchamp even incorporated the
derivation of the word 'kinetic' into his artwork-the
term has the same root as 'cinematic'-with the creation
of his 1926 film Anemic Cinema. The puns written on the
Unfoldings
Rotoreliefs in the film parallel the puns expressed in the
concepts of the work itself (note, for example, that
'anemic' is an anagram of 'cinema').
illusion or on a clockwork-like or motorized mechanism,
but depends instead on something outside itself to set it
in motion.
Examples of kinetic art that I find particularly relevant to
this discussion, combining kineticism, mathematics,
physics, playfulness, and aesthetics, are the mobiles of
Calder and the sculptures of George RIckey. One of the
magic things about these works is that the movement
originates outside the piece, from the touch of wind and
the pull of gravity
Calder credits Duchamp with the naming of his
sculptures:
I asked him [Marcel Duchamp] what sort of a name I could
give these things and he at once produced 'mobile.' In
addition to something that moves, in French it also means
motive. [27]
Rotorelief by Duchamp
The works I wish to consider in the final phase of this
discussion are those in which the change in an artwork
depends not on the eye's perception of two-dimensional
Calder's mobiles have always seemed to me both
otherworldly and organic, the disks of some of them
evoking silhouetted schools of strange fish that might
drift and circle in the turbid atmosphere of Venus, others
of them seeming like trunks and leaves of trees that might
grow on Mars. A Calder mobile about 15 feet high sat off
to one side on a plaza that I crossed every day when I was
an undergraduate in Connecticut. It always looked both
graceful and silly, its tapering red base and black, yellow,
and white plates gently swaying, a stark contrast to the
concrete and granite around it and to the massiveness and
solemn solidity of the enormous concert hall that served
as its backdrop. It acted as a visual reminder that not
everything had to be serious, fixed, and weighty. Calder
made the marvelous comment:
The Role of Play in the Visual Arts
When everything goes right a mobile is a piece of poetry that
dances with the joy of life and surprises. [28]
In Jean-Paul Sartre's preface to the Galerie Louis Carre
catalog for a 1946 exhibition of Calder's mobiles, there
appears the description:
[The mobiles are] a pure play of movement in the sense that
we speak of a pure play of light.... at once lyrical inventions,
technical combinations of an almost mathematical quality
and sensitive symbols of Nature. [29]
George Rickey mentions Calder's mobiles among the
early influences for his own work:
I had made some tentative and playful experiments with
movement, in an Air Corps workshop. Late in 1949 I began
working in three dimensions, or rather four. Calder, whose
work I had known for a decade, had shown that an art of
movement was possible, though I soon found that I could not
accept his limits for myself. [30]
Rickey's sculptures remind me of the apparently
precarious yet controlled balance of a gyroscope, or of a
dancer on pointe: indeed, Rickey has described himself as
a kind of choreographer. In the catalog notes for Rickey's
installation at Boston's Institute of Contemporary Art in
1964, ICA director Sue Thurman described his sculptures'
mesmerizing effect (emphasis hers):
[Rickey] sculpturally projects into free space thinnish pieces of
metal, usually steel, and he does so in such a way that the
component parts move-indeed, that they must move,
granted natural settings wherein air moves at random. He
even sees that they move in ways which are really not
predictable by the viewer, and virtually not repetitive.
Children and cats-all of both groups-are captivated by the
result. Rickey has noticed this. I think it can also be assumed
that no adults, whatever their individual tastes for sculpture,
are unappreciative of the process.... [Tihe kinetic sculptures
now on exhibition were hard to make, and ... are easy to
watch. [31]
Rickey is himself captivated by the forces expressed in his
work: the implications of energy-contained-in-mass
provided by 20th century Physics, the expressive qualities
of motion. He is also very much aware that artists can
easily fall into the trap of incorporating these influences
to produce works with novelty but no depth, his
warnings recalling the admonishments written by
Kandinsky a half century earlier (see page 48). He stresses
that the kinetic artist should always be aware of nature's
lessons:
[Nature] is source book, example, competitor, analogy, tyrant,
seducer, and also inexorable adversary. Nature has offered to
the artist's eye landscape, figure, still life, and also geometry,
light, intervening space (shallow or deep)-all well
understood since the 15th century, and all fundamentally
static. But nature is also 'natural laws:' gravity, Newton's
laws of motion, the traffic laws of topology, or the laws
permitting the motion of a ship or the trembling of the earth.
Nature is rarely still. All the environment is moving at some
pace or other, in some direction or other, under laws which
are equally a manifestation of nature and a subject for art.
[32]
The last artist I will mention is the one whose works
combine practically all of the elements discussed above:
Yaacov Again. He is a pioneer of kinetic art of the sort
both requiring and prompting movement from the
spectator (his early works predate GRAV by a decade).
Agam states his art to be "in perfect harmony with the
spiritual, scientific and material Reality of the twentieth
century" [33]: with the spiritual because of the element of
irreversible time (and thus the consciousness of death)
Unfoldings
and the sense of living, rather than fixed, reality
expressed in the work; with the scientific because of the
implication of inseparability of space and time; and with
the material because of his conception that any of the
technologies of our century is a worthy tool for the
making of art, whether for making light sculptures, sound
sculptures, fire-and-water sculptures, or even bubble
sculptures. In all of Agam's works, time is a fundamental
element. Agam has said of his work:
The ordinary picture reveals itself to the spectator once only.
The spectator sees everything. If someone listens to music, it
takes place in time. One movement follows another. If
someone reads a book, he cannot read it all at once. He reads
it page by page, because there is duration implicit in it. That
duration does not exist in painting. Some painters, such as
Giotto, at Padua or Assisi, cover the whole side of a church,
but that is only a matter of successive pictures. In my own
work, every work of mine, the spectator can leaf through as if
it were a book. He can listen as if it were music, because it
unfolds in time. And, in contrast to books or music, in most
of the work it is real time, irreversible time, because the work
always reveals itself in an unexpected fashion. [34]
A sense of play is also at the heart of many of Agam's
works:
For Agam the notion of 'play' has never had the familiar
connotations of winning or losing the 'game': it has been a
question of man developing from his own internal resources
an inner, unknown voice. From this perspective play
becomes what he has called an "access to self-consciousness
of freedom." [35]
Agam's work seems to be a pure distillation of much of
the space- and time-play of the previous five centuries:
his "accordion" paintings echo the oblique-view effects of
perspective-anamorphic paintings; his use of geometric
form and of color synthesizes and a harmonizes the
precepts of the schools of abstract art of the early part of
this century with Op Art pattern manipulation; his bubble
sculptures seem to liberate the spirits of the disks of
Calder's mobiles to perform a brief and complex dance.
His transformables, in particular, are all that Huizinga
implied visual art could not be. They have a visual quality
of play, but they add an element beyond all of the other
works described thus far: they must be touched, handled,
moved, so that the spectator is no longer spectator, no
longer only a participant through the creative response
van Doesburg described, but has now become, for the
first time, physical participant, activator, player. The
transformables are so varied in type and in size, from the
wall-mounted peg-boards of graphic elements to the
monumental transformable "linear" sculptures such as
The Hundred Gates, Star of David in Four Dimensions, and Beating
Hearts, and yet they are each in a certain way intimate,
temporal, serious, and playful. They are clearly
sculptures, they are clearly toys.
The Role of Play in the Visual Arts
In Popper's words,
They [represent] not fixed states, but possibilities, or
incitements to play.... He is anxious not to produce mere
'tombstones,' which will record some past experience, but to
represent life, to represent a process of becoming that has no
definitive ending and can be prolonged to infinity. It is this
constant attempt to approach the instant of experience, rather
than confining the artistic statement within the bounds of
definitive plastic form, that unifies Agam's concern with play
activity throughout his career. [361
It is Agam's example I endeavor to follow, for I too want
my sculptures to act as incitements to actual physical
play. Agam has shown that the invitation to the artistic
magic circle is not only possible, despite Huizinga's
predictions, but that the public is more than ready to
accept such an invitation.
The Eighteen Levels
Unfoldings
A roomful of Agam's works
The Role of Play in the Visual Arts
Chapter References
[16]
De Stijl: The FormativeYears, edited by Loeb & Loeb, pp. 58 -9.
(Please see the Bibliography for complete publication
information for book citations.)
[17]
Kandinsky, by Dachting & Taschen, p. 38
[18]
Max Bill by Hattinger, p. 15
[1]
Homo Ludens by Huizinga, p. 165.
[19]
[2]
Ibid, p. 166.
Max Bill, p. 61. This is from the biographic information by
Eduard Huttinger, whose notes about this quote read as
follows:
13]
Ibid.
[4]
Ibid, pp. 166-7.
[5]
Intimate World of Alexander Calder by Marchesseau, pp. 74-5
[6]
Calder's Universe by Lipman, p. 33.
[7]
Calder's Circus by Alexander Calder, p. 124.
[8]
The Intimate World of Alexander Calderby Marchesseau, p. 12.
[9]
The Intimate World of Alexander Calderby Marchesseau,
In the catalogue of the exhibition Zeitprobleme in der Schweizer
Malerei und Plastik(CurrentProblems in Swiss Paintingand
deciphered from figure on p. 67
[10]
See the Philpot and Hendriks catalog for a broad selection of
work by Fluxus artists.
[11]
This is my own translation from the French text of Happenings
and Fluxus by Dreyfus, p. [OOPS].
Sculpture) Max Bill formulated in 1936 the principles of
concrete art, conceived as an elaboration of the ideas Theo
Van Doesburg expressed in 1930 in the publication Art
Concret. He revised his text in 1949 for the introduction to the
catalogue of the exhibition Zurcher Konkrete Kunst (Zurich
Concrete Art) which travelled in Germany. This text is
included in the publication Konkrete Kunst edited by Margit
Staber (in Gesammelte Manifeste by Margit Staber, 1966,
Edition Galerie Press, Saint Gallen)
[20]
Kandinsky by Duchting & Taschen p. 39
[21] .Despite StraightLines by Franqois Bucher and Josef
Albers. This Albers quote from 1942 described a
particular group of lithographs.
[22] Vasarely by Spies, p. 5.
[12]
This material is covered in On the RenaissanceRediscovery of
LinearPerspectiveby Edgerton, pp. 126 - 138.
[23]
From Hoek's article on Mondrian in De Stijl, Loeb & Loeb, ed.,
p. 71
[13]
Perspective boxes are mentioned briefly in Historyof Art by
Janson and in Logic and Design in Art, Science & Mathematics by
Barratt. One of Van Hoogstraten's boxes is shown in detail in
[24]
Ibid, p. 72.
[25]
Groupe de Recherche d'Art Visuel, p. 2 (my translation from the
original French).
Anamorphoses: Games of Perceptionand Illusion in Art by Schuyt
[14]
and Elffers.
[26]
Ibid, p. 9.
From Anamorphoses: Games of Perception and Illusion in Art by
[27]
Calder's Universe, by Lipman, p. 268.
[28]
Calder's Universe, by Lipman, p. 261.
Schuyt and Elffers, caption for Figure 8.
[151
Ibid, note for Plate 67.
Unfoldings, Draft 6, 5/8/92
[29]
Ibid.
[30]
George Rickey: Skulpturen, Material,Technik, by George Rickey, p.
29.
[31]
George Rickey: Kinetic Sculptures, catalog of the Institute of
Contemporary art.
[32]
[33]
Ibid.
Le Mouvement (The Movement), catalog of the Galerie Denise
Rene, p. 13.
[34] Agam by Popper, p. 139
[35] Ibid.
[36] Ibid, p. 141.
Figure Credits
Page 41: Calder roaring with the Circus lion, 1971, Calder's
Universe by Lipman, p. 63.
Page 41: Chess Set designed by Bauhaus teacher Josef
Hartwig, 1924, from Bauhaus by Whitford, p. 149.
Page 42: Teeny and Marcel Duchamp's chess set, The
Intimate World of Alexander Calderby Marchesseau, p. 67.
Page 48: Small Worlds VI by Wassily Kandinsky from
Kandinsky by Duchting, p. 68.
Page 49: Variation 1 of "fifteen variations on a single
theme" by Max Bill and Page 49: Variation 2 of
"fifteen variations on a single theme" from Max Bill by
Huttinger, pp. 70 -71.
Page 51: Vega by Vasarely, 1857 by Victor Vasarely, from
History of Art by Janson, p. 680.
Page 54: Rotorelief by Duchamp from Le Mouvement,
The Movement, Galerie Denise Rend, p. 27.
Page 57: The Eigteen Levels, from Agam by Popper, fig 291.
Page 58: A roomful of Agam's works, from Agam, by
Popper, fig 457.
Framework
The sculptures that comprise the project part of my thesis
are one expression of my own ideas about the relationship
between form, pattern, transformation, and playfulness.
My perceptions of this relationship have been the basis of
most of my artistic work, and my ideas about this
relationship are still developing and evolving. The
following sections document my discoveries and
opinions over the past few years, and describe the theory
behind the mechanics of my sculptures, which are based
on geometric forms called "jitterbugs," a term invented
by R. Buckminster Fuller.
A Personal Conception of Form
I postulate form as the foundation, the basis of
interpretation in space. This view is reminiscent of the
ancient Greek philosophers, Plato in particular, who
proposed that form was the foundation of everything,
propounding theories of geometric atoms combining
according to the properties of their shapes.
On the other hand, other artists, such as Johannes Itten
and Wassily Kandinsky, have taken color combined with
form as their foundation, however, my interest is in
experiencing space through both vision and touch-it is
form that is common to these modes. Understanding
one's surroundings requires recognition and
categorization of objects and voids: determining which
way is up, what is level or horizontal, what is reachable
and what is unreachable, which spaces can be traversed,
which spaces can be viewed, what is flat, what is curved.
The eye, the middle ear, the hand, the body as a whole all
send information about physical space to the mind to
interpret.
In the plastic arts, spaces often cannot be traversed,
sometimes cannot (or, by convention, should not) be
touched. A barrier to any of the senses creates an
opportunity to play 'tricks' that exploit the limited
perception of the other senses. When a space cannot be
traversed, walked on, or climbed on, the middle ear
cannot test the eye's sense of the vertical and horizontal.
When a space cannot be reached, or when the forms
within a space cannot be touched, the hands, the body,
cannot verify the eye's judgement of levelness, distance,
texture, hardness, softness. The eye becomes the sole
Unfoldings
transmitter, and the mind interprets the eye's signals
through filters of purely visual experience and
expectation.
Visual Pattern
If the forms in an image or sculpture are familiar, or are
geometrically and visually simple, the 'voice' of visual
experience gains power in the mind's effort to analyze the
object. On this basis, the mind creates strong expectations
for which the eye seeks substantiations. This is a quest for
pattern, in which the expectations have to do with
repetitions, with conformance to a known figurative or
abstract shape or sequence of shapes. The eye seeks these
repetitions and looks for symmetries, which are
specialized repetitions. Finding everything in place
according to prediction can produce responses ranging
from calm, resolution, familiarity, and security to stasis,
rigidity, and boredom:
~u...........-.....
Symbolic Forms
In categorizing the elements of a scene, the beholder may
take certain forms as emblems or symbols, images whose
connotations transcend the attributes of shape. I find it
interesting that words for very simple geometric forms
and formal attributes often carry a host of meanings,
particularly slang meanings: "He's a real square." "She's
pretty sharp." "Look at it from this angle." "I want to hear
some straight talk." "That idea's really bent." The very
words 'imagery' and 'figurative language' denote mental
relationships between meaning and shape.
Every culture that has ever made images at all has
developed particular images and patterns that reach the
status of emblems, universally recognized by those within
the culture, but generally meaningless to those who are
outside the culture, and, for those who recognize them,
nearly impossible to divest of their iconographic weight:
In general, patterns and images that attain this
emblematic status share certain traits:
* those who recognize the symbols expect them to
appear in certain places and orientations, but will
recognize the forms even when distorted or shown out
of their usual context, and in colors other than the
standard
e
the majority of those who recognize the pattern or
image may not know the history, origin, or inventor of
the symbol
Framework
- the set of connotations is usually vastly more
complicated than the image
divergence of potentials, as in the forking of a road, and
their convergence, as in the narrowing of a funnel.
While working on my sculptures, I began to recognize
and develop my personal iconography, my own
interpretations of the 'meanings' of certain forms,
particularly pure geometric forms, which have been the
foundation of myriad philosophies for thousands of
years. My personal symbology often differs from the
interpretations of similar forms in various cultures'
pattern systems, including interpretations that are
accepted in Western, predominantly Christian cultures
such as that of the United States. In the discussion below,
traits ascribed to particular shapes are my own creation,
unless specifically stated to be otherwise.
The arms of the angle admit mediation, they share an
inclination toward a specific direction-unlike the
undifferentiated straight line-but still fundamentally
counter each other's pull.
Linear and Planar Figures
The finite straight line, detached from any other figure,
symbolizes conflict, tension, and opposition. The
endpoints strain away from each other, impinging
beyond the line's visible extent. Simultaneously
indicating two directions without attaining either, the line
denotes polarization, indecision, and risk.
The finite bent line, the angle, signifies choice, chance,
alternative, opportunity, option, decision, viewpoint,
perspective. The bend is a 'meeting point,' a balance point
between possibilities. It simultaneously denotes the
I view the triangle as the fundamental closed figure in
two dimensions. The dual triplets of the triangle's vertices
and its edges define a fixed relationship, and are, for me,
the image corresponding to the words specific, definite,
fixed, balanced, set, stable, distinct, established, resolved.
The triangle has the physical property of rigidity, but not,
for me, its negative connotations of stubbornness and
inflexibility. I prefer to think of the attribute as stability or
firmness.
Selecting three non-collinear points simultaneously
establishes a single triangle, circle, and plane.Thus the
circle and the triangle are not independent figures. The
triangle is the seed of the circle, the circle is the perfection
of the triangle's closure and balance. The triangle's three
angles counterbalance each other-any one of them
mediates between the other two, acting as a restraint to
their attempted divergence. The circle is the culmination
Unfoldings
of this mediation, transforming counterbalance into
equanimity.
The triangle is an image tied in my mind to the word
'thus,' meaning both 'in this manner' and 'therefore,' or
'hence,' for my triangle defines not only the space it
encloses ("it is thus here"), but also indicates the
extension of the plane beyond the enclosure ("thus it is
elsewhere"). I attach great importance to the use of a
triangular arrangement of dots in mathematical proof to
mean 'therefore'. . .
0
*
0
*
0
... and to mean 'because':
In my symbol system, the development from straight line,
to bent line, to triangle corresponds to the advance from
struggle to dialogue to concord.
The planar quadrilateral reintroduces discord to the
system because, as a frame, it is not a rigid, stable form. A
square frame confined to the plane can collapse without
its edges changing in length, becoming first a rhombus
and eventually a straight line, unless the frame is braced
by a strut along either of its diagonals.
NL
ZN
It is important in my symbology that the "collapsing" of
the square is visually similar to a series of perspective
views of a square turning in space from the perpendicular
view to the corner-edge-on view, as if we have entered
Abbott's Flatland.The symbolic importance is that a
quadrilateral is an enlargement of a line, a generalization
of opposition-the borderline between conflict and
collapse among factions of human society is tenuous, the
crossing of the border merely a matter of perspective.
The most regular quadrilateral, the square, represents an
escalation of linear polarization, with the four mutuallyperpendicular rays that extend outward from the square's
center indicating an intensification of the line's symbolic
Framework
strain, the rays extending inward from the square's
corners indicating an intensification of conflict.
I am not at all unique in regarding the basic geometric
forms as having specific symbolic meanings and visual
effects. The assignment of meaning to these forms is as
old as geometry itself. Egyptian, Greek, ancient Islamic,
and ancient Chinese cosmological writings all include
mention of the basic planar shapes, but the meanings of
those shapes differ. As an example, according to the
researches of Keith Critchlow, recorded in his book Islamic
Patterns:an analytical and cosmologicalapproach, the fundamental
shapes and meanings of Islamic art develop as follows.
First, there is the point, which symbolizes unity and
source, "the centre-the elusive controlling point of all
forms."[1] The point "departs" from itself, moving in a
specific direction, creating a line. The line rotates around
the original center, creating a circle.
The circle symbolizes another unity:
The circle is not only the perfect expression of justice-
equality in all directions in a finite domain-but also the
most beautiful 'parent' of all the polygons, both containing
and underlying them. [2]
The circle repeats the motion of the point: it departs from
itself in a specific direction, then the outer copy of itself
rotates around the original circle, creating copies of itself
that just touch the "previous" copies. This produces the
equilateral triangle, when three circles appear, and the
hexagon when seven circles appear. These three-circle
and seven-circle groups are considered other unities:
What Critchlow calls "the simultaneous expression of
direction," in which all six of the outer circles "depart"
from the center at once, produces another set of symbols,
and, in one of the intermediate phases, the square first
appears:
Unfoldings
An indefinitely extending pattern emerges made up from the
exact balance of triangles, hexagons and squares. This
integration of the three primal regular shapes that can fill a
plane has significance both as a symbol and as an archetype
of fundamental surface pattern. [31
Turning for a moment to the symbolism of simple
geometric forms in art, Johannes Itten includes in his
book The Elements of Color a section on the relationship
between form and color. He states that "shapes have their
'ethico-aesthetic', expressive values" that must be
considered in relation to color such that the "expressive
qualities of form and color should be synchronized." He
takes as his fundamental forms the square, the triangle,
and the circle, and describes his assignment of
correspondences as follows:
triangle is thought; and the circle is spirit in eternal motion. If
we look for shapes to match the secondary colors, we find the
trapezoid for orange, a spherical triangle for green, and an
ellipse for violet. [4]
In contrast to Itten, I ascribe the essence of motion to the
square, and balance and equanimity to the triangle and
circle respectively. In a sense, however, we both order the
shapes in the same way, assigning the least spiritual
qualities to the square, and the most to the circle. In this
we follow Western, Christian tradition to a certain degree,
echoing the elevation of the triangle, and its association
with the Holy Trinity, and the supremacy of the circle, and
its association with eternity, ultimate Unity, and God.
The square, whose essence is two horizontal and two vertical
intersecting lines of equal length, symbolizes matter, gravity,
and sharp limitation.. . A marked tension is felt when the
straight sides and right angles of the square are drawn and
experienced as motion... The square corresponds to red, the
color of matter. The weight and opacity of red agree with the
static and grave shape of the square.
red
orneyellow
The triangle owes its nature to three intersecting diagonals.
Its acute angles produce an effect of pugnacity and
aggression... It is the symbol of thought, and among colors
its weightless character is matched by lucid yellow.
ellow
green
blue
violet
A circle is the locus of a point moving at constant distance
from a given point in a plane. In contradistinction to the
sharp, tense sensation of motion produced by the square, the
circle generates a feeling of relaxation and smooth motion. It
is the symbol of the spirit, moving undivided within itself...
The incessantly moving circle corresponds among the colors
to transparent blue.
To summarize, the square is resting matter; the radiating
I
red
Based on Figure57 "Association of colors with correspondingshapes", p. 75 of
Itten's Elements of Color
Framework
Planar Jitterbugs: Meditations on the Square
The instability of the square in my symbol system and in
actual, built form introduces two aspects that are essential
in my sculptures: the ring-like connectivity of forms
combined with the possibility of movement.
Unlike the open angle, the self-connected path along the
edges of a quadrilateral produces a specific visual
definition for 'within' and 'without' in relation to the
figure, until the shape's collapse is complete. In transition,
the form combines the aspects of outwardly-directed
strain with inwardly-directed conflict, as shown:
Unfoldings
In the sculptures, I employ a reversal of the collapsing
square's inner space and outer space, making the
bounded area within the quadrilateral into an opening
among other shapes. It becomes a shifting core for a
complex of forms.
Adding more 'holes' and more 'tile' polygons with
suitable hinging produces what I call a panel jitterbug. A
9-square panel jitterbug appears below:
If each rod of a square frame is used as one edge of a
polygon that is coplanar with the square, and if there is
suitable space around the polygons, the resulting form
will 'jitter' around the square 'hole':
In these panel jitterbugs there are two panel groups, one
rotating clockwise, and the other counterclockwise:
The panels of the jitterbug do not all have to be the same,
and the holes do not have to be equilateral. The choice of
a hinging position gets a bit more difficult, but the results
are interesting:
This is the basic idea behind my jitterbug sculptures. If
the outer polygons are panels or tiles rather than being
open frameworks, changing patterns can be created
around collapsing holes. Two examples appear below:
........
.......
........
...
....
.........
.
.
..
..
..
..
..
.
...
...........
......
.....
...
.......
........
.........
........
........
.
....
I...
.........
........
. .........
There are non-rigid frames other than quadrilaterals that
can at as the 'centers' or 'holes' of panel jitterbugs.
Pentagons will work, as will hexagons, and so on.
Framework
The edges of the jitterbug panels need not be straight
lines. So long as panels that will end up being adjacent
have the same edge design and the panels do not interfere
with each other as the jitterbug opens, the jitterbug will
still operate:
One of the things I find most beautiful about the
jitterbugs is the transformation of the negative space
between panels. Since the pattern of the spaces in the
fully-open "regular" jitterbug is the same as the pattern of
the closed jitterbug itself, the moving structure creates an
impression of the underlying tessellation emerging from
nothingness and collapsing back into nothingness:
M
Variations on 2-4-4' symmetry (two-fold centers of
rotation with two different types of four-fold centers of
rotation) will work as long as there aren't "effective
overhangs" that prevent the jitterbug from opening at all.
There are, of course, many ways to build a pattern that
cannot move regardless of where you place the hinges,
but often it is possible to remove certain sections in an
unmovable jitterbug, and produce one that will move:
.11
Unfoldings
The triangular holes
The basic rules for creating a panel jitterbug are:
in this jitterbug
are rigid-the panels
cannot move
I
" the hole polygon must not be rigid
- the panels must not prevent each other from moving
around the holes
" the hinges must be positioned properly.
Leaving out one of the
triangles in the underlying grid produces a
central hole that looks
like a triangle, but is
really a hexagon
Among M. C. Escher's sketches there are a number of
images that could be made into panel jitterbugs by
making his tessellating figures into panels or, in some
cases, by combining two or more of his figures.
Sometimes the figures that will not close as panel
jitterbugs are as interesting as the ones that will:
Sometimes the choice of panel shape combined with the
choice of hinge positions will prevent the jitterbug from
closing completely, and sometimes will prevent it from
being able to move at all if the pieces all lie in the same
plane:
This choice of shapes and hinge.
positions produces interference
'~\
NZ
Pis,~ X
\
~
~
\
\
This choice produces a jItterbug that
'closed' position
does not have a se
Symmetry Work 20, by M. C. Escher
Framework
Curiously enough, one of Salvador Dali's paintings looks
as if it was designed as a jitterbug:
a
'I
A
"Fifty Abstract Pictures which as seen from Two Yards Change into Three
Len ins Masqueradingas Chinese and as seen from Six Yards Appear as the
Head of a Royal Tiger," by Salvador Dali, 1963
Beyond the Plane
Jitterbug pattern based on Symmetry Work 20
Up to now I have discussed only planar figures, since
even three-dimensional panel jitterbugs really only move
in two dimensions (in fact, the more they behave like
two-dimensional forms, the better). Three-dimensional
solids are also important in my symbol system, as they
have been in philosophy and cosmology throughout
recorded history.
Unfoldings
In ancient Greek philosophy, for example, the pentagonal
dodecahedron, a Platonic solid with twelve five-sided
faces, was considered to be a very special form. In his
pentagonal dodecahedron, which fades into space behind
the table, over which is a shadowy image of a torso with
its arms outstretched in protection.
book, An Adventure in Multidimensional Space, Koji Miyazaki
gives a brief account:
The cosmos is filled with ... regular polyhedra. Nevertheless,
the most secret one, the regular dodecahedron, cannot be
seen among them. It is sure that Plato was troubled and
looked devoutly at the deep starry sky, as everyone does. At
such a moment, he understood that the outer shape of the
cosmos, a natural vessel for the four elements, would be
exactly a regular dodecahedron. Various celestial bodies were
attached to its interior. A philosopher of the Middle Ages,
Bacon, wrote in Opus Majus that Plato was correct because
the other four regular polyhedra can be easily inscribed in a
regular dodecahedron.
In Kepler's opinion, the zodiac is separated into 12 because
the cosmos has a regular dodecahedral shape (Harmonices
Mundi). Socrates, too, proposed a dodecahedral cosmos, just
before his death. [5]
In some circles, it was even thought that the
dodecahedron gave those who understood it special
access to sacred information, especially because the
Golden Ratio, a/b = b/(a+b), appears in the
dodecahedron's proportions, and knowledge of the form
was kept secret. Judeo-Christian culture associates the
number five with man (and six with the Devil), and uses
twelve as a fundamental dividing number, tied to the
division of the Jews into twelve tribes, and to the number
of Christ's disciples, so the numerical relationships of the
number and edge-valency of the faces is also somewhat
mystical. Thus it is fitting that, in Dali's painting of "The
Sacrament of the Last Supper," Christ is depicted among
his disciples under a framework that is a portion of a
The Sacrament of the Last Supper, by Dali, 1955
But it is not only the three-dimensional solids that interest
me-there are also three-dimensional jitterbugs, for the
term 'jitterbug' is not my own creation. It was coined by
R. Buckminster Fuller, and first mentioned in one of his
books in 1960:
The jitterbug is simply a vector equilibrium constructed with
flexible joints. When supported, it is a perfect vector
equilibrium consisting of eight triangles and six squares.
When released, however, it contracts symmetrically, going
through a series of phases. It becomes first an icosahedron,
then an octahedron. Ultimately it becomes a tetrahedron.
Framework
A number of people have researched these forms,
including H. E Verheyn (whose article on the theory of
the movement of three-dimensional jitterbugs I
recommend to anyone with a serious interest in the
subject), Professor Arthur Loeb, Bill Varney, Jack Gray,
and Dennis Dreyer.
The 'vector equilibrium' is Fuller's name for the
cuboctahedron, the form obtained by either truncating a
cube down to the midpoints of the original edges, or
truncating an octahedron down to the midpoints of its
original edges.The vertices of this figure lie at the centers
of spheres in one possible spatial closest packing. Fuller's
name for the form derives from his observation that the
distance from the center to any vertex is the same as the
edge-length of both the triangles and the squares in the
figure.
Cuboctahedron
inscribed in an
octahedron
Cuboctahedron
inscribed in a
cube
\VXV.
...
The cuboctahedral frame (by 'frame' I mean a shape made
of rods forming the edges rather than of panels or tiles
forming the faces) is not a rigid structure because of the
squares in the framework.However, in contrast to the
planar square I discussed above, nothing in this figure
restricts the collapse of the squares to planes.
If a flexible square frame is NOT constrained to a plane,
then the struts can become the boundary of a threedimensional form I call a regular tetrad, shown below.
Tetrad and
planes
It's easiest to think of this as a kind of bent wing, like a
very simple paper airplane. It is 'regular' because all the
edges are the same length. The angles of the regular tetrad
that lie between the pair of struts in each plane are
congruent, and I call them the point angles. The angle
between each strut and the line where the two planes
meet I call the base angle, and all the base angles of a
regular tetrad are congruent. The segment in which the
tetrad faces meet I call the diagonal of the tetrad. I call the
dihedral angle of the tetrad the angle between the planes
that the tetrad faces lie in (this is consistent with the
Unfoldings
general use of the term 'dihedral angle').
I
EEFMEESNA
...
The tetrad has its own place among my geometric forms.
It stands in the same relationship to the square as the bent
line segment does to the straight line segment. It signifies
a more harmonious state than the square's orthogonal
opposition-the tension becomes potentiality. The tetrad
is the symbol of folding and unfolding, the shape inherent
in the hinge, the book, the moth. There is a lunar phase,
about three-quarters full, where the moon's disc appears
folded. The essence of a fold is the possibility of opposing
factions meeting, the willingness to compromise, to
acquiesce, to bend. In my symbology, the words 'fold' and
'bend' do not have the connotations of giving in, or of
giving up some measure of power. I regard the ability to
find compromises a kind of strength in itself.
The tetrad frame mediates between two folded surfaces,
called tetrad coverings, which meet around the frame like
a child's hands cupped to capture a firefly:
As with the linear angle, these folded forms balance
divergence (in the spread away from the spine of the
form's 'wings' or 'leaves'), with convergence and
enclosure (in the sheltered inner channel along the spine).
The tetrad represents the process of decision-making,
pondering, considering-the space between the posing of
a problem and its solution.
The tetrad covering surface itself represents a decision
among alternatives, since, starting with a triangle plus
any point outside the triangle, there are three ways to
make a tetrad covering:
Framework
90 degrees, their base angles are decreasing from 45
degrees, and their dihedral angles are decreasing from
180 degrees.
Fuller's cuboctahedral jitterbug's six squares (positioned
in the planes of the six faces of the original cube) will only
hold their square shape if each is cross-braced in a certain
way, or, as Fuller put it, supported:
If the squares are braced incorrectly, the cuboctahedron
can stretch, shrink, or twist in various ways. If the squares
are not braced at all, or, in Fuller's terms, are "released,"
they can all simultaneously begin to collapse into
congruent tetrads. In the following discussion, the tetrad
coverings being described are the ones that keep the outer
form convex. As the cuboctahedral jitterbug's tetrads
begin to collapse, their point angles are decreasing from
There are actually two ways that the cuboctahedron can
collapse. Consider the triangles in the frame. Starting
with any triangle, give it a color. Color all three of its
vertex-wise adjacent triangles with a second color. Each
pair of these three triangles will 'share' a vertex-wiseadjacent triangle. Color these shared triangles with the
original color. These three original-color triangles all
share a single vertex-wise-adjacent triangle that is exactly
opposite and parallel to the starting triangle. Color this
final triangle with the second color. No two vertex-wiseadjacent triangles will be the same color:
When the cuboctahedron collapses one way, the Color 1
triangles rotate clockwise as the squares deform to
tetrads, and the Color 2 triangles rotate counterclockwise.
When the cuboctahedron collapses the other way, the
Color Is rotate counterclockwise, and the Color 2s rotate
clockwise. One of the two possible collapsings appears
below:
M1
Unfoldings
The Symbolism of Jitterbugs
Buckminster Fuller saw the vector equilibrium
(cuboctahedron) jitterbug as a fundamental model of the
way things move in the universe. He derived the vector
equilibrium from a study of closest-packing with spheres,
with the vertices of the cuboctahedron representing the
centers of twelve spheres packed around a central sphere:
When the point angles of all the tetrads are 60 degrees, the
outer form of the object is a regular icosahedron, though
six of the 30 edges of the icosahedron are missing-in
other words, if, at this point, the tetrads were braced
across their diagonals, the bracing struts would be the
same length as the frame struts, and the framework
would be a regular icosahedron.
If the tetrads are allowed to collapse until their point
angles are zero, the outer form of the object is a regular
octahedron with all its edges doubled.
The top and bottom triangles of the octahedron can now
twist to fold the entire structure flat into four equilateral
triangles with their edges quadrupled, and the outer three
triangles of this can be folded up into a tetrahedron:
There are only three possible structural systems in the
universe: tetrahedron, octahedron, and icosahedron. As I
pumped this closest-packed set of 12-around-one, it went
down like that-it went through the icosahedron phasethat's exactly what happened when you took one ball out...
and then it becomes the octahedron. So this vector
equilibrium pumps between the three possible cases of all
structural systems. So you begin to see how it is the
framework of how things happen in nature. [6]
In Synergetics, Fuller restated this belief in the cosmic
fundamentality of the vector equilibrium and of its
movement in one of his classic convoluted sentences. I
have quoted it below as if it were a poem:
The vector equilibrium's jitterbugging
conceptually manifests
that any action (and its inherent reaction force)
applied to any system
always articulates a complex
of vector equilibria macro-micro jitterbugging
involving all the vector equilibria's ever cosmically replete
complementations
by their always co-occurring internal and external
octahedra-
This shift to the tetrahedron marks a connection between
my symbol system and Fuller's, explained below.
Framework
all of which respond to the action
by intertransforming in concert
from 'space nothingnesses'
into closest-packed spherical 'somethings'
and vice versa
in complex three-way shuttle
while propagating a total omniradiant wave pulsation
operating in unique frequencies
which in no-wise interfere
with the always omni-co-ocurring cosmic gamut
of otherly frequenced cosmic vector-equilibrium
accommodations. [7]
So, although Fuller concerned himself only with threedimensional vector equilibrium, and I concern myself
primarily with two-dimensional ones, we look at the
forms in the same way, as an extension of the magic
inherent in geometry itself. Both I and Fuller also ascribe
special properties to the tetrahedron and octahedron.
In my symbology, the tetrahedron is the fundamental
closed ( rm in three dimensions. As with the planar
triangle, the tetrahedron signifies resolution, this time in
the form of containment, centeredness, contentment,
confidence, gathering, condensation, focus, channelling,
distillation. The tetrahedron is the simplest of the Platonic
solids, with only four faces, four vertices, and six edges. It
is self-dual: connecting the centers of a tetrahedron's faces
produces a smaller tetrahedron. It represents complete
concurrence, in that every vertex connects along a single
edge to every other, and every face meets every other.
The tetrahedron is a stable form, even when built as a
framework instead of a solid. In the lotus position, the
human body echoes tetrahedral form, head erect, hands
resting palm-up on the knees, weight distributed on the
triangle of the buttocks and crossed legs. I liken the
resolution and calm of meditation to the symbolic power
of the tetrahedron.
Unfoldings
In each pair of tetrad coverings, the segments forming the
spines (diagonals) of the coverings are skew-orthogonal,
meaning they are at right angles to each other, but are not
in the same plane. A transparent regular tetrahedron
viewed along one of its planes of mirror symmetry looks
like a square with its diagonals drawn in:
Buddha statue
The tetrahedral frame mediates among three pairs of
tetrad coverings, since there are three ways to associate
tetrads with a given tetrahedron:
The tetrahedron thus resolves the conflict of the square,
reshaping flat opposition into a balance among
alternatives.
Selecting four non-coplanar points simultaneously
establishes a unique tetrahedron and circumscribed
Framework
sphere, and 'establishes' three-dimensional space. The
tetrahedron is the seed of the space we inhabit, its stable
foundation.
generating triangle to the resulting triangle of the
octagon-as-antiprism. Thus the hexagon symbolizes an
intermediary, translator, or bridge.
The final symbolic figures I will discuss here are the
triangular prism, the triangular antiprism, and the
hexagon:
The prism represents the direct, blunt, and stubborn, the
triangle advancing through space with a fixed orientation
and direction, without regard for any contingencies or
limitations. The figure is not rigid when built as a
framework-the rectangular 'sides' of the framework
collapse. Symbolically, this indicates the folly of pure
obstinacy.
The antiprism combines perseverance with resilience, the
triangle advancing through space in a fixed direction, but
changing its orientation in order to accommodate change,
and to accept support. An antiprism's framework is
stable, since the supports are all triangular. The
octahedron, a regular antiprism, balances purpose,
perseverance, independence, and support.
A transparent regular octahedron, seen face-on, appears
as a hexagon with two inscribed triangles. The outer
hexagon comes from the zig-zag structure connecting the
As a final note, I discovered that, in one of the generative
figures in Critchlow's discussion of Islamic cosmology,
where the three regular planar shapes, the triangle,
square, and hexagon, all appear in a single tiling pattern,
the patter works as a jitterbug:
That these three shapes appear together, and that they
happen to work as a jitterbug, takes on a special
significance for me, taking on a meaning related to the
symbolic meanings of the individual shapes.The starting
formation represents an unstable community, comprising
centers of conflict among areas of fixed, well-established
views, and liaisons or intermediaries among the factions.
The closing of the jitterbug represents the resolution of
Unfoldings
conflicts, the working out of disputes-it becomes a
beautiful symbol of hope for our world.
The symbolic significances are part of the personal,
internal drive to explore these shapes sculpturally, and,
particularly, to explore them as kinetic objects, in which I
can express my impressions of their shifting meaning in
relation to one another, as I will show in the next chapter.
Framework
Chapter References
(Please refer to the Bibliography for complete ?blishing
information for book citations)
[1] Islamic Patterns by Critchlow, p. 9.
[2] Ibid.
[3] Ibid, p. 20.
[4] The Elements of Color by Johannes Itten, pp. 75-6.
[51 An Adventure in MultidimensionalSpace by Miyazaki,
pp. 12-13.
[6] Fuller to Verner Smythe, NYC, Reel 2, p. 1, 25 Feb, '69.
[7] Synergetics, R. Buckminster Fuller and the Synergetics
Institute.
Figure Credits
Page 70: Symmetry Work 20, by M. C. Escher, Escher on
Escher: Exploring the Infinite, p. 37.
Page 71: "Fifty Abstract Pictures which as seen from Two
Yards Change into Three Lenins Masquerading as
Chinese and as seen from Six Yards Appear as the
Head of a Royal Tiger," by Salvador Dali,
1963Gallery of Modern Art, p. 135
Page 72: The Sacrament of the Last Supper, by Dali, 1955,
Salvador Dali, Maddox, p. 86.
Page 78: Buddha statue, front cover, Dhammapada,
Easwaran.
Unfoldings
Jitterbug Sculptures
I make jitterbug sculptures in order to explore and
express several themes:
e
the way one responds to and understands a changing
pattern
* the power of the moment of recognition of an image
e
sensations of confusion and comprehension, the
appearance of chaos, the appearance of order
* the symbolic significance of a hinge point
* the essence of rotation, an angle changing
One idea that underlies my work is that chaos and order
are matters of perception. What one doesn't understand
and cannot predict is both meaningless and chaotic-this
concept is contained in the very meaning of the words.
Discovering a pattern within a chaotic system changes its
character-it ceases to be chaotic. I allege that the
majority of human intellectual endeavor constitutes a
search for this patter, this order. In the special endeavors
of play and art-making, human beings feel free to create
order based only on our individual perception: we find
patterns within objects and do not require those patterns
to match established norms or follow logical principles;
we assign meaning and symbolic power to those patterns
according to our personal rules; we impose order and
sense upon a situation without demanding acceptance or
understanding from those outside a special circle.
Another idea I explore is that discovery consists of
realizing that one understands, of recognizing that,
through logic or through intuition, one has already found
a pattern. But there is a special experience before finding
the pattern, at that moment when it is just beyond one's
grasp, felt rather than found, and then, as in play, "all is
movement, change, alternation, succession, association,
separation"(see quote, page 16).
The jitterbug's form is simple, but its movement is
unfamiliar, and the effect of its movement on surface
patterns is difficult enough to predict that it plunges the
participant into that moment-before-discovery, that
moment of confusion and anticipation.
The magic thing about jitterbugs is their movement, and
that is, unfortunately, the hardest aspect to convey about
Unfold mgs
them in text and still images, particularly line drawings
and scanned photographs. Unlike Op Artists, I am trying
to convey a sense of time for an image of a real object
rather than constructing an image from "anonymous and
homogeneous forms" to elicit a different time-awareness.
I will present a series of pictures of the forms in the stages
of their movement but then the reader must try to
animate them.
cluster of buildings, like a pueblo, or a city-scape when
the sunset gleams off of skyscrapers of metal and glass.
Depending on the way the previous viewer left the
sculpture, the boxes will either appear to be clustered
haphazardly, or will appear to line up on an invisible
Cartesian grid.
For my final thesis project, I created several jitterbug
sculptures. My aim was to create objects that resonate
with the magic of the jitterbug's movement, yet which are
simple enough to make that magic comprehensible after a
few minutes of experimentation. I intend the sculptures to
be picked up and manipulated, so they are reasonably
small and lightweight.
I work in wood, plexiglas, metal, and glass, contrasting
transparency with opacity, and playing visual openness
against actual openness.
Mirage
Mirage is a jitterbug made of 12 brass tubes with a square
cross-section, open on the top and bottom, with insets of
stained glass. Closed, the sculpture stands 4 inches high,
and is 8 x 8 inches across and when fully open it is
approximately 11 x 11 inches across. The display stand for
the piece is a light-table made of poplar, plexiglas, and
glass.
The satin-finished brass tubes or open boxes range in
height from 2 inches to 3 1/2 inches. The top edges of the
tubes rise unevenly from the edges to the center of the
jitterbug, so that, seen from the side, the piece resembles a
The insets mix very dark areas with very light areas,
echoing the alternating sense of simplicity and
complexity, clarity and obscurity, that the viewer
experiences upon handling the piece. What begins as a
mysterious, complex mesh becomes a simple square grid,
and then dissolves into complexity again, resisting the
JitterbugSculptures
viewer's attempts to grasp the pattern of its movement
and the shift of the inner pattern.
The glass insets are recessed in the boxes, so the viewer
approaching the sculpture first sees fragments of pattern
reflected in hints of yellow and red, and in areas of light
and dark at the top of the boxes.
/
These glimpses of color invite the viewer to look as
straight down onto the sculpture as possible, giving the
best view of the pattern and its underlying structure, but,
at the same time, producing reflections inside the brass
boxes, some matching the patterns in adjacent boxes,
some differing.
In designing this piece, I was inspired, and, at times
haunted, by very personal meanings, symbols, and
images. Some elements of the sculpture derive from
idiosyncratic expressions of facets of my family history, of
my Christian heredity, of the presence of Native
Americans among my ancestors. Some of these influences
are easy to identify in the finished piece, some are hidden.
Consider the following connections: the twelve boxes of
the jitterbug hinge together in the shape of a cross around
five openings, with four of the openings opening one way,
and the last opening the other:
Unfoldings
associate with the form of the square. I also sought a
strongly geometric form, but one based not on the various
traditions of geometric form in art described elsewhere in
this thesis, but one which was tied to my own history, to
my own experience, memories, and creative methods. I
found inspiration in a Navajo rug design, and felt a
confirmation of the power of that inspiration in the
discovery that, after developing my own design using the
essence of the rug pattern, I produced a figure that acts in
consonance with the very nature of the jitterbug. When
the cluster closes one way, the energy of the pattern points
inward:
The combination of 12 and 5 relates this jitterbug form to
the numerology of the dodecahedron, and the shape of
the cross ties it to Christian symbolism. The pieces cannot
be connected in any way other than this and still operate
as a jitterbug, so the four openings that move the same
way, each touching one corner of the central, unique
opening, are essential to the working of the jitterbug. As I
looked at those four spaces while designing the form,
they took on a mystical significance, related in my
subconscious to the symbolism of the cross: without my
consciously deciding on their meaning, they became
symbols of the writers of the four Gospels, Matthew,
Mark, Luke, and John, four bridges to a central unity.
In designing the stained glass pattern, I sought a pattern
that would express the idea of shift inherent in the
jitterbug structure as well as the idea of opposition I
Closed the other way, the pattern not only points
outward, but contains, mirrored within it, a design akin to
another Native American pattern symbolizing the power
of the eagle:
JitterbugSculptures
IN,
Basic pattern for Spirit Spiral
Spirit Spiral has
a jitterbug structure based on three-fold
symmetry. The piece is made of Honduran mahogany
and plexiglas, and has a carved surface pattern. Closed,
the sculpture is 8 inches across, and is half an inch thick.
The surface pattern (not shown) was inspired by several
images: galaxies turning in an expanding universe; spiral
swirls carved in the metal of ancient Celtic bronze mirrors
and battle ornaments; and Ursula K. LeGuin's description
of the Hinge of a valley town she envisioned for her book
Always Coming Home. I
include the full description here for
several reasons, first, because the symbolic meaning of a
hinge in LeGuin's invented culture so closely resembles
Unfoldings
my own conception, and second, because I love the way
she writes about it:
I found, at last, the town I had been hunting for. After
digging in several wrong places for over a year and
persisting in several blockheaded opinions-that it must be
walled, with one gate, for instance-I was studying yet once
more the contours of my map of the region, when it dawned
as slowly and certainly as the sun itself upon me that the
town was there, between the creeks, under my feet the whole
time. And there was never a wall; what on earth did they
need a wall for? What I had taken for the gate was the bridge
across the meeting of the creeks. And the sacred buildings
and the dancing place not in the center of town, for the center
is the Hinge, but over in their own arm of the double spiral,
the right arm, of course-there in the pasture below the barn.
And so it is, and so it is. [1]
LeGuin describes the importance of the hinge in her
description of a fundamental word in the language, called
t
40
U,'
Kesh, which she ascribes to the people of the town:
Heyiya: The first element of this word, hey- or heya, is the
untranslatable statement of praise/greeting /holiness/being
sacred.
The second is the word iya. This means a hinge: the piece of
hardware or leather that connect a door to the opening it
doses and opens. Connotations and metaphors duster thick
to this image. Iya is the center of a spiral, the source of a
gyring motion; hence a source of change, as well as a
connection. Iya is the eternal beginning, the process of energy
arising and continuing. The word for energy is iye. [2]
The central turn of the jitterbug seems to have the effect of
a secondary spin at the three extremes of the form, as if
the outer edges responded to some centrifugal force
trying to whirl them away. The dramatic explosion of the
central triangle in the piece is energy unlocked.
..........
............
Jitterbug Sculptures
When the piece is part-way open, the direction of the
apparent "spin" of the central space changes from
clockwise to counterclockwise, and the piece begins to fall
back on itself. Unlike the Miragejitterbug, the ending shape
is not the same as the beginning shape-there is a
development of form as well as of pattern. This is the
quality that evoked galactic imagery-sudden expansion,
and eventual recompression, gathering back the farflung
pieces into a new form. The same burst symbolizes a flash
of intuition followed by deeper, calmer understanding.
Jitterblocks
The final piece is called litterblocks and is the most
traditionally toy-like of my recent sculptures. It started
out as a tool for experimenting with stained glass patterns
for Mirage, but it took on a life of its own.
My idea was to make a structure that I could easily drop
patterned squares into, observe their pattern
transformation, and take them out again. I wanted it to be
an interesting and pleasing object on its own, but it had a
very specific "practical purpose," to use Huizinga's term
(see quote on page 39). This object became a kind of
personal test of Huizinga's claim that the aesthetic
impulse does not enter into the making of a functional
piece.
The making of Jitterblocks
The criteria for the object were:
* the surface pattern and its transformation through the
jitterbug movement had to be the strongest visual
element-the base, the construction method, and the
textures could not draw attention to themselves.
- the pieces had to be relatively easy to manufacture,
sturdy, small enough to handle very easily and to
carry around with me.
* it had to be cheap to make
I decided that the easiest way to make the base would be
to start with some object that was already a kind of small
square "well" that would be easy to hinge to adjacent
pieces. This was where practical concerns and aesthetic
impulse first combined: it mattered to me on a practical
level that the piece operate smoothly because, if the
movement was clumsy, it would attract more attention
than the transformation of the pattern, so all of the twelve
pieces of the base had to have the same cross-section
dimensions. However, the next concern was aesthetic: it
mattered to me that they not just be a close enough match
not to draw attention away from the pattern, but that they
be a perfect match, which meant I had to find something
that could be obtained cheaply as an identical dozen. The
solution was to use 1"xl" plastic pillboxes from a local
crafts store. I chose black so that the base would drop into
the background.
Unfoldings
with designs drawn on them. Most of them fell right out
again when I turned the base upside down, making the
patterns easy to examine and change. But I became
frustrated with the flimsyness of the paper, and with the
difficulty of changing only one of the cells at a time, so I
made a set of blocks, cut to size from a poplar board, and I
painted them with patterns derived from the conflict lines
that I imagine within the squares, making the patterns on
each side connect with patterns on adjacent faces. Having
six patterns on each block allowed me to expand my
pattern experiments within the jitterbug. An interesting
side effect of using blocks was that now I had a set of
small sculptural elements that were interesting even
when they weren't in the base:
The hinging method had similar constraints: it had to
make the movement smooth, to be as unobtrusive as
possible, and as sturdy and easy to do as possible. The
solution: I drilled holes in the corners of the boxes and
tied through them with dental floss, which I then stained
black with ink. Practicality would have dictated that I
drill all the corners of the boxes, since the drill-holes
barely showed from the sides, and didn't show at all from
the top, allowing me to mass produce the boxes and not
have to take a lot of time worrying about whether I was
hinging the right pair of pieces during assembly.
Aesthetics, however, dictated otherwise, and it was the
aesthetic impulse I followed. I drilled only the minimum
number of holes needed.
With the base done, the next concern was the objects to
drop into the boxes. At first, I used small squares of paper
I now found that I wanted to make more blocks, to create
patterns that had nothing to do with pattern experiments
for Mirage. The jitterblocks had now become a sculpture in
their own right, providing a final, personal proof that
play, mathematics, and art do, indeed, meet.
JitterbugSculptures
Chapter References
(Please see the Bibliography for complete publishing
information for all book citations)
[1]
Always Coming Home by Ursula K. LeGuin, p. 3.
[2]
Ibid, p. 525.
Unfoldings
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Table 1: Arts and Artists
Author
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Year
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Editions Denise Ren6
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Author
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Publisher
City
Year
Escher, M. C.
Escher on Escher: Exploring the Infinite
Harry N. Abrams, Inc.
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New York, NY
1986
Fry, Edward F.
Cubism
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1945
Gerstner, Karl
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elements
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Cambridge, MA
1986
Hendriks, Jon
Fluxus Codex
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Huttinger, Eduard
Max Bill
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Institute of Contemporary
Art
George Rickey: Kinetic Sculptures
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Itten, Johannes
The Elements of Color
Van Nostrand Reinhold
New York, NY
1970
Janson, H. W.
History of Art, 2nd Edition
Prentice-Hall Inc. and Harry
N. Abrams
New York, NY
1977
Lipman, Jean
Calder's Universe
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1976
Loeb, Arthur L. and
Loeb, Charlotte I.
(translators)
De Stijl: The Formative Years
The MIT Press
Cambridge, MA
1982
Locher, J. L.
The World of M. C. Escher
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Abrams, Inc, Publishers
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1971
Maddox, Conroy
Salvador Dali: 1904-1989: Eccentricand Genius
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Year
Kinetic Art: Theory and Practice:Selections from
the Journal Leonardo
Dover Publications, Inc.
New York, NY
1974
Marchesseau, Daniel
The Intimate World of Alexander Calder
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1989
Marchiori, Guiseppe
La Sculpture de Berrocal
La Connaissance
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1973
New York Gallery of Modern
Art Including the
Huntington Hartford
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Salvador Dali 1910-1965
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1965
Oster, Gerald
"OpticalArt" (article)
Applied Optics, Vol 4, No 11,
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Parinaud, Andr6
The Unspeakable Confesssions of Salvador Dali
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Phillpot, Clive and Hendriks,
Jon
Fluxus: Selections from the Gilbertand Lila
Silverman Collection
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New York, NY
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Picton, John, and Mack, John
African Textiles
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1989
Pollitt, J. J.
Art and Experience in Classical Greece
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1972
Popper, Frank
Agam
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Rickey, George
Skulpturen, Material,Technik
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Berlin, C'r rmany
1979
Soby, James Thrall
Salvador Dali
The Museum of Modern Art
New York, NY
1941
Scully, Vincent
The Earth, The Temple, and the Gods: Greek
Sacred Architecture
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1979
Spies, Werner
Vasarely
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1970
Author
Malina, Frank
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Table 1: Arts and Artists (Continued)
Table 2: Mathematics in Art; Perspective; Pattern
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Title
Publisher
City
Year
Barratt, Krome
Logic and Design in Art, Science, and
Mathematics
Design Press, Divsion of TAB
BOOKS Inc.
New York, NY
1980
Blatt, Sidney J.
Continuity and Change in Art: The Development
of Modes of Representation
L. Erlbaum
Hillsdale, NJ
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Carraher, Ronald G.
Optical Illusions and the Visual Arts
Reinhold Publishing Corp
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Edgerton, Samuel Y, Jr.
The Renaissance Rediscovery of Linear
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Fuller, R. Buckminster
Synergetics dictionary:The Mind of Buckminster
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Grunbaum, Branko, and
Shephard, G. C.
Tilings and Patterns
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1987
Henderson, Linda Dalrymple
The Fourth Dimension and Non-Euclidean
Geometry in Modern Art
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Princeton, NJ
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Kappraff, Jay
Connections:The GeometricalBridge Between
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Pedoe, Dan
Geometry and the Visual Arts
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Schuyt, Michael & Elffers,
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Anamorphoses: Games of Perceptionand Illusion
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Stevens, Peter S.
Handbook of Regular Patterns:An Introduction
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City
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Artin, Michael
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Dunham, William
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Hildebrandt, Stefan &
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Holden, Alan
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Huntley, H. E.
The Divine Proportion:A Study in Mathematical
Beauty
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Kline, Morris
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An Adventure in MultidiemsionalSpace: The Art
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Polytopes
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Polya, G.
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Eliade, Mircea
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Table 5: Play, Toys, Games, and Puzzles
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Coffin, Stewart
The Puzzling World of PolyhedralDissections
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Grunfeld, Frederic V.
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1985
100
Index
Symbols
'because' dots 64
art-making
and physical distance 17
art-object as play-object 40-45
'therefore' dots 64
Baudelaire 22
abstract art 18
Albers, Josef 50
Bauhaus 18
goals of school 18
Josef Hartwig 41
Alhazen 45
because symbol 64
anamorphoses
chinese 47
French 47
Turkish 47
Bill, Max
definition of Concrete Art 48
Fifteen variations on a single theme 49
Agam, Yaacov 23
angle
literal meaning 62
personal meaning 63
anti-art 18
Brecht, George
games 44
brick wall 62
Bronx Zoo 40
Brunelleschi 45
Unfoldings
Bull's Head 21
C
Calder
and toy manufacturers 40
as playboy 41
grand-neice Nanette 41
kitchen utensils 41
Calder, Alexander 16, 19
chess set box and pawns 41
circus 40
Circus lion 41
Firemen's dinnerfor Brancusi 17
cards 44
Central Park Zoo 40
chess
Saito
jewel chess 43
nut and bolt 43
smell chess 43
sound chess 43
spice chess 44
weight chess 44
chess sets 41
Calder's box and pawns 41
Fluxus artist sets 42
Takako Saito's set 42
Teeny and Marcel Duchamp 41
chesspieces
all-white set by Yoko Ono 44
made by Calder from checkers and bolts 42
made by Saito from grinding wheels 43
made by Takako Saito from bolts 43
poem by Man Ray 42
Chinese anamorphic painting 47
Chinese cosmology 65
Christian culture 63
Christian geometry 66
Christian heredity 85
Christian symbolism
and dodecahedron 86
Christopher Robin 20
circle
Islamic meaning 65
Itten's meaning 66
personal meaning 63
relation to triangle 63
Concrete Art 48
conflict 64
creative response
in art 48
creativity
of artist 23
of spectator 23
Critchlow, Keith 65
102
Index
cross 85
F
cylinder anamorphosis 47
Flatland 64
D
Dada 18
and play 18
Dali, Salvador 23
difference between games and toys 19
FLUXKIT 18
Fluxus 18
chess sets 42
games 42-45
magazines 42
The Art/Game of 44
dodecahedron 86
Fluxus attitude
codex by Maciunas 44
doll houses 40
FLUXYEAR boxes 19
Duchamp, Marcel 41
and Dada 18
influence on Fluxus 44
ready-mades 21
freedom
in play 14
Duchamp, Teeny 41
E
Egyptian geometry 65
emblems 62
ergo symbol 64
French anamorphic painting 47
Fuller, R. Buckminster 61
G
Galen 45
games 19
Monopoly 20
Euclid 45
games and toys
differences between 19
Europanism
and Fluxus 18
GRAV52
and Op Art 52
Evans, Walker 19
Greek geometry 65
eyeglasses 40
Groupe de Recherche d'Art Visuel 52
103
Unfoldings, Draft 6, 5/8/92
J
Hartwig, Josef
chess set 41
jewelry
by Calder 40
hexagon
Islamic meaning 65
Jonah and the whale 46
hinge
symbolic significance 83
Holbein the Younger 46
The Ambassadors 46
holy mathematics 47
Homo Ludens 13
Huizinga, Johan 13
interlude
defined 15
play as ~ 15
intermezzo
play as ~ in real life 15
intuition 15
Jones, Spike
influence on Fluxus 44
K
Kandinsky, Wassily 47, 48, 61
Small Worlds VI 48
King of Spades 44
Kruger, Dolf 16
line
as collapsed quadrilateral 64
Islamic meaning 65
personal meaning 63
lion
in Calder's Circus 41
invention 21
invitation to join magic circle
in play 14
Islamic cosmology 65
Itten, Johannes 61
M
Maciunas, George
Fluxus codex 44
Maciunas,George
and Fluxus magazines 42
Index
magazines 43
Op Art 50
magic circle 14
in art 22
of play 14
opposition 64
Man Ray
text for Duchamp's chess set 42
Masaccio 45
Milne, A. A. 21
order
play and 19
types of order in play 19
types of order wihtin play
social order 19
types of order within play
structural order 19
Mondrian, Piet 47
Monopoly 20
P
myth 14
pawns
See chesspieces
N
Native American ancestors 85
perspective
one-point 45
two-point 46
Native American pattern 86
perspective box 46
Navajo rug design 86
Picasso, Pablo 21
New Testament Gospels 86
picture puzzle 46
nose masks 40
Olympic rings 62
Ono, Yoko
chess set
chess sets
Yoko Ono's set 44
105
Unfoldings, Draft 6, 5/8/92
play
and Dada 18
and dance 13
and limitation in space 16
and limitation in time 16
and music 13
and myth 13
and order 19
and real life 15
and risk 16
and ritual 13, 14
and tension 16
and volition 14
as celebration 16
basic characteristics 13-16
in the open 16
play and creativity 13
Q
quadrilateral, planar
personal meaning 64
R
Ready-Mades 18, 21
rhombus
relation to planar quadrilateral and square 64
risk in play 16
ritual
and play 14
rules 19
of games 20
of toys 20
playing cards 44
point
Islamic meaning 65
Pooh 20
Winnie the Pooh
see Pooh
Poohsticks 21
Ptolemy 45
puzzles
Fluxus 44
106
Saito, Takako
chess set 42
School of Delft 46
space
analysing using the body 61
spatial limitations 45
spice chess 44
Index
square
Islamic meaning 65
Itten's meaning 66
personal meaning 64
slang meaning 62
symmetry 62
T
tension in play 16
U
United States
cultural pattern systems 63
unity
Christian 66
connection to Islamic geometry 65
V
therefore symbol 64
van Doesburg, Thdo 15, 23
and Concrete Art 48
toy manufacturers
and Calder 40
van Hoogstraten, Samuel 46
toys 19
sculptural toys 40
transportive quality of art-making 15-16
Vasarely, Victor
and Op Art 50
Vega 51
visual pattern 62
transportive quality of play 15
triangle
Christian meaning 66
Itten's meaning 66
personal meaning 63
z
Zoos 40
triangle, equilateral
Islamic meaning 65
Turkish anamorphic painting 47
Twenty Questions 19
107
Unfoldings, Draft 6, 5/8/92
108